


^ 
^ 



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3 0^ 



ECONOMIC CYCLES: THEIR LAW 
AND CAUSE 



THE MACMILLAN COMPANY 

NEW YORK • BOSTON • CHICAGO • DALLAS 
ATLANTA • SAN FRANCISCO 

MACMILLAN & CO., Limiteo 

LONDON • BOMBAY • CALCUTTA 
MELBOURNE 

THE MACMILLAN CO. OF CANADA, Ljd. 

TORONTO 



ECONOMIC CYCLES: THEIR 

LAW AND CAUSE 



BY 
HENRY LUDWELL MOORE 

PROFESSOR OF POLITICAL ECONOMY IN COLUMBIA UNIVERSITY 
AUTHOR OF " LAWS OF WAGES " 



" Nous croyons en effet, pour notre part, que 
pour avancer vraiment dans la connaissance 
6conomique, il faut s'attaquer directement et 
d'abord, a des variations, c'cst-a-dire a la forme 
dynamique des phenomenes, par la voie ex- 
p^rimentale." Francois Simiand. 



THE MACMILLAN COMPANY 
1914 

All rights reserved 



3 31 W 



Copyright, 1914 
By the MACMILLAN COMPANY 
Published December, 1914. 



h'r 



DEC 10 1914 






TO 

JANE MOORE 

A CRITIC WHO NEVER DISHEARTENS 
A CO-WORKER WHO KEEPS THE FAITH 



CONTENTS 

CHAPTER I 



Introduction 



CHAPTER II 



CYCLES OF RAINFALL 



The Use of Fourier's Tlieoreni 6 

Periodogram of Rainfall 14 

The Equation to the Rainfall Curve 21 

Rainfall in the Corn Belt 26 



CHAPTER III 

RAINFALL AND THE CROPS 

The Secular Trend in the Yield of the Crops 35 

Critical Periods of Growth 41 

Cycles in the Yield of the Representative Crops and the 

Corresponding Cycles of Rainfall 44 

Cycles in the Index of Crop Fluctuations and in the Corre- 
sponding Index of Mean Effective Rainfall 49 



CHAPTER IV 

THE LAW OF DEMAND 

The Theory of Demand 02 

Statistical Laws of Demand 06 

The Prediction of Prices 77 

Elasticit^'^ of Demand 82 

vii 



viii Contents 



CHAPTER V 

THE MECHANISM OF CYCLES 

The Prices of Agricultural Commodities Correlated with the 

Yield of the Several Crops 94 

Rising and Falling Prices as Related to Yield-Price Curves . 100 

The Volume of the Crops and the Activity of Industry . . 103 

A New Type of Demand Curves 110 

The Fundamental, Persistent Cause of Economic Cycles . . 116 



CHAPTER VI 

SUMMARY AND CONCLUSIONS 135 



ECONOMIC CYCLES: THEIR LAW 
AND CAUSE 



CHAPTER I 
INTRODUCTION 

There is a considerable unanimity of opinion among 
experts that, from the purely economic point of view, 
the most general and characteristic phenomenon of a 
changing society is the ebb and flow of economic life, 
the alternation of energetic, buoyant activity with a 
spiritless, depressed and uncertain drifting. During the 
creative period of the rhythmic change each factor in 
production receives an augmenting income, and the 
mutual adjustment of interests in the productive 
process is brought about in a natural way, primarily 
through the operation of competitive law. The period 
of decline in the cycle presents a sharply contrasted 
aspect of industry. With the organization of capital 
and labor at first unchanged, the amount of the product 
falls; each of the interested factors seeks at least to 
retain its absolute share of the product; friction and 
strife ensue with a threatening of the disruption of 
industry. WTiat is the cause of this alternation of 
periods of activity and depression? What is its law? 
These are the fundamental problems of economic 
dynamics the solution of which is offered in this Essay. 

Pohtical Economy began to make progress in a 
rational way when the Physiocrats put forth their 
doctrine of the dependence of all forms of economic life 

1 



2 Economic Cycles: Their Law and Cause 

upon agriculture. Another momentous step was taken 
in the direction of theoretical development when the 
English economists formulated the law of diminishing 
returns in agriculture and traced its all-pervasive 
influence in the production and distribution of the 
product of industry. The desideratum of economic 
dynamics at the present time is the discovery of a law 
that shall be to a changing society what the law of 
diminishing returns in agriculture is to a society in a 
comparatively static condition. 

The full truth in the old Physiocratic doctrine has 
not been exploited. The Department of Agriculture 
of the United States reaffirms the central idea of the 
doctrine in its motto: ''Agriculture is the Foundation 
of Manufacture and Commerce/' and in the spirit of 
this motto it publishes invaluable statistical data. 

It is proverbial that the farmer is at the mercy of the 
weather. If it be true that the explanation of economic 
cycles is to be found in the law of supply of agricultural 
products, it is surely wise in a study of rhythmic eco- 
nomic changes to inquire whether the law of the chang- 
ing supply of raw material is not associated with a law of 
changing weather. Is there a well-defined law of chang- 
ing weather? 

Supposing that it is possible to discover that the 
weather passes through cycles of definite periods and 
definite amplitudes, it will then be necessary to show 
how the crops are affected by the weather and how the 
cycles of the weather are reproduced in cycles of the 
yield of the principal crops. 



Introduction 3 

When the changes in the physical yield of the crops 
are shown to be dependent upon changes in the weather, 
the next stage in the investigation is to connect the 
yield with its value, and this brings one face to face 
with another unsolved problem in theoretical economics. 
The most recent phase of economic theory opens with a 
description of the "law of demand," which from the 
time of Cournot, Dupuit, and Gossen has been assumed 
in all theoretical discussions, but there has been no 
method for finding the statistical equation to the law. 
It will be necessary to overcome the difficulties of this 
problem before a solution can be offered of the more 
fundamental inquiry as to the law and cause of cycles in 
economic phenomena. 

When the physical yield of the crops has, on th^e one 
hand, been related to the cycles of the weather and, on 
the other, to the prices of the respective crops, it will 
then be possible to take the final step and to show how 
the cycles in the physical yield of the crops produce the 
cycles in the activity of industry and the cycles of 
general prices, and how, finally, the law of the cycles of 
the crops is the law of Economic Cycles. 



CHAPTER II 

CYCLES OF RAINFALL 

"The first thing that in my opinion ought to be done towards 
making the observations useful for scientific purposes is to perform 
that kind of more perfect averaging which is afforded by the har- 
monic analysis. There is a certain amount of averaging done, but 
that is chiefly daily averages, with monthly averages, and yearly 
averages; but the more perfect averaging of the harmonic analysis 
would give the level of the variation of the phenomenon." 

— Lord Kelvin, in his testimony before the Meteorological Com- 
mittee of the Royal Society, 1876. 

From the point of view of the relation of changing 
weather to the varying fruitfulness of agriculture, the 
most important factors that are usually included in 
the term, weather, are temperature and rainfall. We 
begin our investigation with this common belief and 
inquire, in this chapter, whether the varying amount 
of annual rainfall is subject to any simple law. 

In order to carry forward the inquiry as to the exist- 
ence of a law of annual rainfall an analysis must be 
made of a long record of precipitation. Our choice of 
a record is limited by two conditions: First, our object 
in investigating the periodicity of rainfall is the hope 
of throwing light upon the periodicity in the yield of 
the crops, and this expectation obviously makes it 
desirable that the record of rainfall shall be as repre- 
sentative as possible of the conditions of precipitation 

4 



Cycles of Rainfall 5 

in our leading crop area; secondly, as the existing 
meteorological records are of unequal lengths and of 
varying reliability, it is necessary to take the best long 
records that can be found within the limits of the crop 
area. 

The principal region of grain production in the United 
States is in the Mississippi Valley, but the meteoro- 
logical records of the Middle West do not extend through 
a long period of time. In order to achieve the two ends 
of having a long record of precipitation and of having 
the record typical of the conditions in the grain area, 
the device has been adopted of investigating rainfall in 
the Ohio Valley — which affords the longest record ob- 
tainable in the neighborhood of the central Mississippi 
region — and of showing that the rainfall of our lead- 
ing grain state, Illinois, follows the same law as the 
rainfall of the Ohio Valley. 

The stations in the Ohio Valley with long rainfall 
records are Marietta, Portsmouth, and Cincinnati. 
Their mean annual rainfall since 1839 is given in 
Table I ^ of the Appendix to this chapter. The graph 
of the course of rainfall in the Ohio Valley since 1839 
is traced with other graphs on Figures 4, 5, and 6. The 
problem that must now be faced is the question as to 
whether the sequence of annual rainfall in the Ohio 
Valley follows a simple law, and if so, to give a quanti- 
tative formulation of the law. 

1 The data were taken from Bulletin W of the Weather Bureau of 
the United States and from the Ajintial Reports of the Chief of the 
Weather Bureau. 



6 Economic Cycles: Their Law and Cause 

The Use of Fourier's Theorem 

A preliminary examination of the rainfall data of the 
Ohio Valley leads to the conclusion that there is prob- 
ably no secular trend to the data, that is to say, there 
is probably no tendency of the rainfall to increase con- 
tinuously or to decrease continuously with the flow of 
time. It is true that when the amount of rainfall is 
correlated with time, the coefficient of correlation is 
r = — .227 ± .075, where the coefficient is three times its 
probable error and is therefore suggestive of a decrease 
in the amount of rainfall with the flow of time. More- 
over, if a straight line is fitted to the data, the indicated 
annual decrease in the rainfall is seven hundredths of 
an inch. But these facts are no justification for hold- 
ing to a secular decrease in the amount of annual 
rainfall. For, in the first place, if there are cycles in 
the amount of the rainfall, the low degree of the ob- 
served correlation might be due to the data of rainfall 
including incomplete cycles; in the second place, the 
record is drawn from only three stations and because 
of the limited number of stations might give an acciden- 
tal, low degree of correlation between amount of rain- 
fall and time; and in the third place, improvements 
in the method of taking the observations might have 
introduced changes that would account for the ob- 
served small annual decrease in the amount of rain- 
fall. In view of these considerations, it is probably 
best to proceed with our problem on the assumption 
that there is no secular trend in the amount of annual 



Cycles of Rainfall 7 

rainfall. If this assumption is true, it follows that, in 
all probability, the course of rainfall in the Ohio Valley, 
is cyclical, or a combination of cycles. 

In an inductive treatment of any form of rhythmic 
or cyclical change it is necessary that the method 
adopted shall satisfy two conditions: (1) It shall be 
consistent with recognized mathematical processes; 
(2) It shall afford means of testing the degree of proba- 
bility that the results are not chance phenomena. 
Unless the method rests clearly upon an approved 
mathematical process, it is scarcely possible to say 
whether the attained results may not be entirely formal ; 
and unless the findings are tested for the degree of their 
probability, there is no assurance that the adduced 
cycle may not be a chance occurrence. The literature 
in which rhythmic phenomena are treated in a statis- 
tical way teems with fallacies and uncertainties that 
illustrate the need of observing the above conditions; 
for the method frequently adopted of smoothing the 
data is so arbitrary that one is at a loss to know whether, 
after all, the alleged periodicity may not, in fact, be due 
to the process of smoothing; and, in addition, one is 
left in doubt as to whether an indefinite number of 
cycles other than the particular one adduced might not, 
with equal or greater probability, be obtained from the 
same data. 

The method that was employed to reach the results 
of this chapter rests upon the analysis invented by 
Joseph Fourier,^ which is called, in English treatises, 

1 The most philosophic exposition of Fourier's theorem is in 




8 Economic Cycles: Their Law and Cause 

harmonic analysis. The perfection of the method 
whereby the findings may be subjected to the test of 
probabihty is the work of Professor Arthur Schuster ^ 
of Manchester. 

We may begin the presentation of the method with a 
definition of a series of terms that constantly recur in 

the treatment of periodic phe- 
nomena. Figure 1 will facili- 
tate the exposition by affording 
a graphic description of the 
terms dealt with. 

Suppose that the point Q 
moves uniformly in the circle 
of Figure 1 , that is to say, sup- 
pose that the point Q describes 
equal arcs in equal times and, therefore, proportional 
arcs in different times. Then, if the measurements of 
the arcs of the circle are made from the point A and 
the reckoning of time is begun when Q is at E, the 
angle A O E is called the angle at epoch, or simply 

Fourier's o^v^^ work: Theorie ancdytique de la chaleur. In Freeman's 
English translation the treatment is found on pp. 137-212. 

^ The fundamental memoirs of Professor Schuster are 

''On the Investigation of Hidden Periodicities with Application 
to a Supposed 26 Day Period of Meteorological Phenomena." 
Terrestrial Magnetism for March, 1898. 

"The Periodogram of Magnetic Declination as obtained from the 
records of the Greenwich Obsen^atory during the years 1871-1895." 
Camh'idge Philosophical Society Transactions, Vol. 18, 1899. 

"On the Periodicity of Sunspots." Philosophical Transactions of 
the Royal Society of London, A, Vol. 206, 1906. 

"The Periodogram and its Optical Analogy." Proceedings of 
the Royal Society of London, A, Vol. 77, 1906. 



Cycles of Rainfall 9 

the epoch of the uniform circular motion. The 
radius of the circle is the amplitude of the motion; 
the time of going once around the circle is the 
period of the motion; the ratio of A Q to the 
circumference of the circle is the phase of the mo- 
tion. 

If from each position of Q a perpendicular is dropped 
upon the diameter of the circle, G H, the foot of the 
perpendicular will describe a simple harmonic motion. 
The amplitude of the simple harmonic motion is one- 
half of the range of the motion, that is, one-half of G H, 
or the radius of the circle. The period of the simple 
harmonic motion is the interval between the passing 
of the point P twice through the same position in the 
same direction. The distance of the point P from the 
middle of its range, 0, is a smiple harmonic function 
of the time, P = y = a s'm (nt+e) , where a is the radius 
of the circle — or the amphtude of the simple harmonic 
motion — e is the angle of epoch, and n is the angle de- 
scribed by the moving point Q in the unit of time. The 
period of the simple harmonic motion is, in the above 

27r T^^ , . nt + e 
case, — . Its phase is —7^ — . 

Figure 2 presents a graph of simple harmonic mo- 
tion. As in Figure 1, the point Q moves uniformly in 
the circle ; the point P performs simple harmonic motion 
according to the formula y^^a sin {ni-\-e), where a is 
the amplitude of the motion, or radius of the circle, e 
is the angle of the epoch, namely, A E, and n is the 
arc described by Q in the unit of time. If time is meas- 



10 



Economic Cycles: Their Law and Cause 



ured upon the line B C, the sinuous curve of Figure 2 
is the graph of the function, y =asin (nt+e). 



/ p 


'^\„ 


/ 


\ 










\Q 


r 




/ 






^,-— -"^'^ A 


B 1 


Z 


\ J 


A 


s 


je 




/ 








\ 




/ 


V 


J 








^Vy^^ _ 










^ 


y 



Figure 2. 

The importance of simple harmonic functions in 
the study of periodic phenomena grows out of the fact 
that any periodic curve however complex ^ can be ex- 
pressed mathematically by a series of simple harmonic 
functions. By the help of Fourier's analysis a periodic 
function may be put in the form 

(1) y =^o + fli cos kt + a., cos 2 ki + ag cos Zki^ . . . 
+ 6i sin ki + 60 sin 2 fc^ + 63 sin 3 A;f + . . . 

If in (1), we put, 

ai = A^ sin e^'i ^2 = -^2 sin e<i\ a^ = ^3 sin e^] &c., 
61 = Aj cos e^; 62 = A2 cos 62', 63 = A3 cos e^; &c., 

We get, 

(2) y = Ao+Ai sin (A;^ + gj) + Ao sin (2 kt + 63) 
+ A3 sin {dkt + e^) + . . . 

where y is expressed as a series of sines. In a similar 

manner, equation (1) may be expressed as a series of 

cosines, 

' Tlie few exceptions to the general rule are discussed in the 
mathematical texts that develop Fourier's theorem. 



Cycles of Rainfall 1 1 

(S) y -- Ao + Bi cos (kt - e i) + B., cos {2kt-e 2) 
+ 53COS(3 kt-e^) + . . . 

In the use of Fourier's theorem for the purpose of 
analyzing periodic phenomena, we follow a process 
analogous to the use of Taylor's theorem in the simpler 
demonstrations of mathematical economics. By far 
the greater part of Cournot's pioneer treatise and of 
subsequent work of his school is based upon the as- 
sumption that, if the economic function under investi- 
gation is y=f{x), then f{x-{-h) may be expanded by 
Taylor's theorem, and the first terms of the series may 
be used as an approximation to the form oi f{x). Simi- 
larly, in our use of Fourier's series, the attention will be 
focussed upon a few harmonics as a first approximation 
to the solution of the problem in hand of expressing 
in mathematical form the periodicity of annual rainfall. 

Assuming that any periodic function may be ex- 
pressed as a Fourier series, the problem is presented of 
determining the values of the coefficients. The series, 
as we know, is of the form 

y = / (0 == Aq + tti COS kt + a^ COS 2kt+... 
4- hy sin kt + 62 sin 2 kt-\- . . . 

What are the values of the first term and of the co- 
efficients of the sines and cosines? In order to deduce 
the necessary values, we shall have need of the follow- 
ing lemma: 

If m and n are two unequal integers and A: is put equal 
to -^, then 



12 Economic Cycles: Their Law and Cause 

I cos mkt cos nkt dt = 0, 

o 

/T 
sill mkt sin nkt dt = 0, 

o 

/T 
sin wfc< cos wA;f dt = 0. 

o 

The lemma may be proved to be true by evaluating the 
three integrals according to the usual methods. The 
first integral, for example, becomes 

/T /»T 

COS mkt cos nkt dt = l / | cos (m—n) kt +cob (m+n) kt\dt 

o o 

[sin (m-n) kt sin (m + n) ktX^ 
" L 2 {m-n) k '^ 2 (m + n) k Jo 

But k = -^, and, consequently, I cos wA:< cos n/cf d^ = 0. 

o 

With the aid of this lemma we may proceed to evalu- 
ate the coefficients in Fourier's series. If we integrate 
the series between the hmits a and T, we get, 

f (t) dt = Ao I dt + ai j cos kt dt + h^ j sin ktdt+ . . . 

o o o o 

But all of the terms except the first on the right-hand 
side of the equation will vanish, and consequently 

J7 (t) dt 
f/ {t) dt = A, J^dt = A, T, or A^ = -^ 

o o 

Since j f{t)dt is the area of the original curve for one 

o 

whole period T, the constant term in Fourier's series is 
equal to the value of the mean ordinate of the original 
curve. 



Cycles of Rainfall 13 

To determine the value of Oi, multiply throughout 
by cos A:^ and integrate between limits o and T. 

I f (t) Qos kt dt = A^ I coskidt + oi I cos^ ktdt 

o o ' o ■ 

sin kt cos kt dt + . . . 

o 

Or / / (0 cos kt dt = a^ I cos2 kt dt, since / cos kt dt and 
/ sin kt cos kt dt are both equal to zero and all the other 

o 

terms on the right-hand side of the equation, according 
to our lemma, disappear. But 



n ,7.^. pi + cos 2 A:^,^ , r^ sin 2 An ^ 

o o 

and as a result, we have 



/T 
/ (0 COS 
II- o 

<^i "9 = / / (0 COS kt dt, or Oj = 2 — 



ktdt 



T 

Therefore ai is equal to twice the mean value of the 
product /(O cos kt. 

In a similar manner the value of any other coefficient 
may be determined. Take, for example, 6„. Multiply 
throughout by sin nkt and integrate between o and T, 

I f {t) sin 7ikt dt = On I S!n2 nkt dt = b„ j ^- — — dt = 

o o o 

f J sin2nA:n ^] . T 

/T 
• Therefore b^ 



14 Economic Cycles: Their Law and Cause 

is equal to twice the mean value of the product 
f{t) sin nkt. 

Having found the algebraic values of the coefficients 
in Fourier's series, we may now proceed to determine 
their statistical equivalents in the case of annual rainfall. 

The Periodogram of Rainfall 

If the length of a cycle of rainfall were known before- 
hand, the preceding exposition of Fourier's theorem 
would suffice to determine, from the data of precipita- 
tion, the amplitudes and phases of the harmonic con- 
stituents of the Fourier series descriptive of the rainfall 
cycle. But in the problem before us of analyzing the 
rainfall data of the Ohio Valley, we do not know whether 
there are many cycles or only one cycle or, indeed, 
whether there are any cycles at all. And there is no 
short method of solving the problem. 

Suppose, for example, it were assumed from a priori 
considerations that the amount of rainfall is affected 
by sunspots, and, as sunspots are known to occur in 
periods of about eleven years, suppose it should be in- 
ferred that the annual rainfall will likewise show a period 
of eleven years. If the rainfall data of the Ohio Valley 
are examined for an eleven years period, it will be found 
that the data yield a definite amplitude and a definite 
phase for a cycle of eleven years, but this fact is no 
warrant for holding that there is a true rainfall period of 
eleven years. Every other grouping of the seventy- two 
years record will likewise show a definite amplitude 



Cycles of Rainfall 15 

and a definite phase. The questions that one is in- 
terested to have answered are: (1) What is the law of 
the distribution of Fourier coefficients when the data 
are analyzed for all possible periods; and (2) how may 
the true cycles be separated from the accidental, 
spurious cycles that are obtained when the data are 
exhaustively analyzed? 

In Figure 3 the results of a detailed, laborious ex- 
amination of the data of annual rainfall in the Ohio 
Valley are presented in graphic form. On the axis of 
abscissas are measured, within assigned limits, the 
possible lengths of cycles in the 72 years of rainfall. 
By extending the calculations to 36 years, we obtain 
for the assumed periods a record of possible recur- 
rences varying from 2, in case of the period of 36 
years, to 24, in case of the period of 3 years. On the 
axis of ordinates are measured the squares of the co- 
efficients of the first harmonic in the Fourier series 
corresponding to the lengths of periods recorded on 
the axis of abscissas. The numerical values of these 
squares are given in the fourth and eighth columns of 
Table II in the Appendix to this chapter. The method 
of deriving the values may be illustrated by taking the 
cycle ofj 8 years. Suppose, as a first approximation, 
that the equation to Fourier's series is put in the alge- 
braic form 

y = F{t) = A^ + a^ cos kt + hi sin kt = A^-ir A^ sin (fcf + e)- . 

Then the corresponding arithmetical values derived 
from the Ohio rainfall data are 



16 



Economic Cycles: Their Law and Cause 




l/pjuiQj JO ssi^oui ui dpn^ijduje 3i/jjo djenbg 



Cycles of Rainfall 17 

y = F(t) = 41.19-3.13 cos'^t + 2.69 sin ^ t 

o o 

= 41.19+4.13 sin (~ t + 310° 41'). 

The values of the terms a\, 6,, A\ are respectively 
(3.1339)2, (2.6938)-, (4.1325)^, and these values are 
given in the proper columns of Table II in the Ap- 
pendix. In Figure 3, the values oi A^ for the several 
periods are measured on the axis of ordinates. 

An examination of Figure 3 will illustrate the truth of 
a statement advanced a moment ago. It is clear from 
the course of the periodograph ^ that if one were to 
take any period at random between the limits of 3 
years and 36 years, he would in every case obtain a 
finite value for the amphtude of the selected cycle ; and 
if, by chance, selection should fall upon, say, 18, or 21, or 
29, or 36 years, an argument might be made with some 
degree of plausibility that a real cycle had been dis- 
covered. But, in truth, the real significance of no one 
cycle taken at random can be judged apart from its 
place in the distribution of all the cycles that can be 
derived from the data. 

This last point is of fundamental importance. The 
only object of investigating cycles of rainfall or cycles of 
economic phenomena is that the knowledge of the 

> The terms periodograph and periodogram were coined by Pro- 
fessor Schuster. 

The periodograph is the cun-e tracing the values of A^; the 
periodogram is the surface between the periodograph and the base 
line giving the lengths of the periods. Schuster: "The Period- 
ogram of Magnetic Declination," p. 108. 



18 Economic Cycles: Their Law and Cause 

constant recurrence of the cycles may place one in a 
position to foresee and utilize the dependent phenomena. 
But the control of phenomena dependent upon a cycle 
presupposes that the cycle is itself a real phenomenon 
with a natural cause, and that consequently it persists 
with an increase in the number of observations. If, 
however, an apparent cycle of any length taken at 
random is obtained from the given data, one would 
surely misspend his time if he were to set about the 
search for its cause, and were to derive conclusions based 
upon the hypothesis of the persistence of the cause. 
The cycles due to formal, accidental causes must be 
discriminated from the cycles with natural causes. 

The separation of true cycles from spurious or 
accidental cycles is facihtated by the periodogram ^ of 
observations. If, following Professor Schuster, we call 
the square of the amplitude of any given period the 
"intensity" of the period, then it may be said that the 
probabihty of the reality of a period is dependent upon 
the ratio of its intensity to the mean intensity of the 
periodogram. Or, again following Professor Schuster, 
if we call the mean intensity of the periodogram the 
'^expectancy," then the reality of a period is dependent 
upon the ratio of its intensity to the expectancy of the 
periodogram. For instance, if in case of a given period 
the ratio of intensity to expectancy is, say, 3 to 1, then 
in about one case in twenty we should expect to obtain 
by chance a greater amplitude than the amplitude of 
the particular period in question. If, on the other hand, 
1 See the preceding note. 



Cycles of Rainfall 19 

the ratio were say, 7 to 1, a greater ratio would not 
occur by chance once in a thousand times. ^ 

With these facts in mind, let us again examine Fig- 
ure 3. It is clear that the principal periods needing 
attention are those respectively of 8, 29, 33, 36 years. 
In case of the 8 year cycle there can be very little 
doubt as to the existence of a true periodicity approx- 
imating 8 years in length. The ratio of the square of 
its amplitude to the mean square amplitude of the 
periodogram is 6.71 to 1. We may accordingly accept 
with considerable confidence the existence of a natural 
period of rainfall in the Ohio Valley approximating 
8 years in length. 

The cycle of 33 years, inasmuch as the ratio of the 
square of its amplitude to the mean square amplitude 
of the periodogram is 3.27 to 1 is in all probability a 
true cycle. The doubt that exists is due to the smallness 
of the ratio and the few recurrences — only two ^ — 

1 Schuster: "The Periodogram of Magnetic Declination," pp. 124- 
125. 

2 Those who deprecate the use of such meager data should con- 
sider well the testimony of Lord Kehan before the Meteorological 
Committee of the Royal Society, 1876. 

Question 1710. "The sum which parhament will give for this 
purpose being a limited sum, do you think that it would be well to 
reduce the number of observations in order to have more money to 
spend upon the reduction of obsers-ations? / think at all events imtil 
one eleven years period, the s^rn spot period, is completed, it ivould be 
wrong to reduce the nuviher of observations." 

Question 1735. "Supposing that you had one of these analyses 
calculated for a period of 11 years, would each year's observ'ations 
and still more each period of 11 years obser\-ations, require to be 
introduced into this analysis so that you would have an analysis of 
22 years, and an analysis of 33 years, and so on from time to time, 



20 Economic Cycles: Their Law and Cause 

that our data afford. A greater confidence in the exist- 
ence of a real period of 33 years is given by the fact that 
Bruckner ^ claims to have found a true period of about 
35 years in an examination of a vast mass of rainfall 
material all over the world. Accordingly, the existence 
in the Ohio Valley of a real 33 years period of rainfall we 
shall assume to be very probable. 

The other two periods of 29 years and 36 years are 
not easily disposed of. But in the first place, the ratios 
of the squares of the respective ampUtudes to the mean 
square amplitude of the periodogram are not such as to 
justify the acceptance, with any degree of confidence, of 
the existence of true cycles of 29 years and 36 years. 
In the second place, they are both so close to the period 
of 33 years as to cause a doubt as to whether they may 
not be spurious periods that are likely to appear in the 
neighborhood of a real period.- 

Considering the short range of our data it would not 
be properly cautious to press the point of the existence 
of any definite real cycle. But this much is certain: 
If there are true cycles in the data of the 72 years of 
rainfall in the Ohio Valley, there is far greater prob- 
ability that two cycles are those of 8 years and 33 
years than of any other round numbers between 3 and 

or, being done, would it be done once for all? / cannot say whether 
anything with reference to Terrestrial Meteorology is done once for all. 
I think probably the work will never be done." 

1 Edward Bruckner: Klimaschwankungen seit 1700. Bruckner's 
period fluctuates greatly in length and has an average value of 35 
years. 

2 Schuster: "The Periodogram of Magnetic Declination," p. 130. 



Cycles of Rainfall 21 

36 years. Moreover, the periods of 8 years and 33 
years afford the most probable basis derivable from the 
data upon which to reason both as to the future course 
of rainfall in the Ohio Valley and as to the course of the 
phenomena dependent upon rainfall. 

Assuming, then, that for the purpose in hand, the 33 
years and 8 years periods are the most probable and 
valuable, we turn to the consideration of the equation 
to the graph giving the course of rainfall in the Ohio 
Valley. 

The Equation to the Rainfall Curve 

It will be helpful to approach the algebraic descrip- 
tion of the cychcal movement of rainfall in the Ohio 
Valley, by observing how we obtain an increasingly 
accurate account of the actual rainfall by superposing 
the constituent cycles. We shall use, as an index of the 
relative fit of the several curves, the root-mean-square 
deviation of the observations from each curve. 

If, as a preliminary step, the raw data of the course 
of annual rainfall are examined, it is found that the 
mean annual rainfall in the Ohio Valley is 41.19 inches, 
and the root-mean-square deviation about the mean is 
/S = 6.70 inches. 

If the long 33 years cycle is considered by itself, it 
appears that the root-mean-square deviation about the 
33 years curve is >S=6.39 inches. The graph of the 
33 years cycle is given in Figure 4. Its equation is 

y = 41.19 + 2.88 sin /|^ t + 328° 7'V 



22 Econoviic Cycles: Their Law. and Cause 




ssi^oui ui iiejuiej jenuuy 



Cycles of Rainfall 23 

the origin being at 1839. This curve traces in bold 
outline the general course of ramfall. It gives the 
ground-swell of the rainfall movement. 

If the 8 years cycle is superposed upon the 33 years 
cycle, the root-mean-square deviation about the curve 
becomes S = 5.66 inches. The graph of the combination 
of these two curves is traced in Figure 5. Its equation is 

2/ = 41.19 + 2.88 sin (1^^ + 328° 7') +4.13 sin (|^^ + 310°4rV 

the origin being at 1839. A point of interest with regard 
to the flow of the curve is the rapidity with which it 
rises from the least minimum to the greatest maximum, 
and the slowness with which it then descends to the 
subsequent least minimum. 

If the 8 years cycle and its semiharmonic of 4 years 
are combined with the 33 years cycle and its semi- 
harmonic of 16.5 years, the root-mean-square deviation 
about the compound curve becomes aS = 5.29 inches. 
The graph of the curve is given in Figure 6. Its equa- 
tion is 

2/=41.19 + 2.88 sin^l^ < + 328" 7') + 2.25 sin (1^ ^ + 271° 42'") 

+ 4.13 sin/^^ + 310° 41'W 2.14 sin^^^+ 180° 28'V 

the origin being at 1839. In this closer approximation 
the characteristic rapid rise to a general maximum and 
slow fall to a general minimum is reproduced. Another 
characteristic is the longer interval that the curve 



24 



Economic Cycles: Their Law and Cause 




^ Si 



Cycles of Rainfall 



25 




mjoui ui ijp^uipj /enuu^ 



26 Economic Cycles: Their Law and Cause 

lingers at the minima and the short period during which 
it flows in the neighborhood of the maxima.^ 

Rainfall in the Corn Belt 
Thus far we have dealt with the law of rainfall only 
in the Ohio Valley. The object in taking the Ohio 
data, rather than the data of a state more representa- 
tive of the leading cereal area, was to make an investiga- 
tion of a longer meteorological record than is afforded 
by the data of the central Mississippi Valley. But our 
purpose in dealing with meteorological records at all is 
to show the dependence of crops upon the cyclical 
movement of the elements of the weather. We must, 
therefore, prove that the cycles of rainfall which we have 

1 1 should like to make clear the method I have followed in the 
derivation of the equations to the curves. My object was to obtain 
a summary description of the general course of rainfall in order that 
I might discover, later on, whether the characteristic general fea- 
tures of the movement of rainfall are reproduced in the changing 
yield per acre of the crops. As a first step I tried to detect the real 
cycles in rainfall and I believe I have shown that, if the 72 years 
record is sufficiently long to reveal the true cycles, then the most 
probable lengths of the cycles are, in round numbers, 33 years and 
8 years respectively. With so short a range of data I regarded it as 
useless to attempt to calculate the lengths of the periods to a greater 
degree of precision. I next had to derive the equations to the curves 
showing the characteristic general course of rainfall, and it seemed 
to me that, for this purpose, the method described in the text for 
evaluating the coefficients in a Fourier series might properly be 
used. If the 33 years cycle were taken as the fundamental cycle, 
then the 8 years cycle would be approximately the fourth harmonic 
in the series, and the 4 years cycle would be the eighth harmonic. 

The arithmetical process for computing the coefficients is indi- 
cated by Professor Schuster in Hidden Periodicities, pp. 13, 14 and is 
briefly described by Professor Perry in an article on "Harmonic 
Analysis" in The Electrician, for February 5, 1892. 



Cycles of Rainfall 27 

discovered for the Ohio Valley are likewise the cycles 
that exist in the heart of the grain producing area. 

Among the states of the Middle West, lUinois is 
probably the most highly representative of American 
cereal production. It produces the largest crop of 
corn,^ which is the leading American cereal, and it 
ranks second in the production of oats. Most of the 
other cereals that are produced in the upper Mississippi 
Valley are hkewise cultivated with success in lUinois. 
Another fact that makes Illinois a desirable state for 
our purpose is that its meteorological records are fairly 
long and are obtainable from so many stations as to be 
representative of the weather conditions in the entire 
state. This last fact is all-important if the statistics 
for crop production of the whole state are to be con- 
sidered in relation to the weather cycles of the state. 

In Table III of the Appendix to this chapter the 
record of the annual rainfall in Illinois is given for a 
period of 41 years. ^ The ideal direct method with 

^ This statement was accurate when it was first written. But in 
1912 Iowa gained by a narrow margin the first place among the com 
producing states. 

2 The raw data were taken from Bulletin W of the Weather Bu- 
reau of the United States and from the Anmial Reports of the Chief 
of the Weather Bureau. The stations used in computing the mean 
annual rainfall were: — In Northern Illinois: Aurora, Cambridge, 
Chicago, Tiskilwa, Galva, Kishwaukee, Ottawa, Winnebago, and 
Henry. In Central lUinois: Charleston, Carlinville, Coatsburg, 
Decatur, GriggsviUe, Knoxville, Havana, LaHarpe, Pana, Peoria, 
and Springfield. In Southern Illinois: Cairo, Cobden, Carlyle, 
Golconda, Flora, GreenviUe, McLeansboro, Mascoutah, Mt. 
Camiel, and Palestine. 

All of these stations do not present full records for the 41 years, 



28 Economic Cycles: Their Law and Cause 

reference to these data would be to compute the 
periodogram in the same manner in which it was com- 
puted in the case of the Ohio Valley data, and then com- 
pare the periodograms. But this method has not been 
followed. A less direct, and far less laborious, process 
has been adopted. We know from the Ohio data that 
there are two cycles of rainfall, a 33 years cycle and an 8 
years cycle, and we know, furthermore, that when the 
curve for rainfall in the Ohio Valley is computed for the 
33 years and 8 years periods and their semiharmonics, a 
good fit to the data is obtained. The questions that are 
asked with reference to the Illinois data are these: 
If we assume the existence of a 33 years period and an 
8 years period in the Illinois rainfall data, will the 
rainfall curve fit the Ilhnois data as well as the Ohio 
curve fits the Ohio data? Will the IlUnois curve re- 
produce the characteristic features of the Ohio curve? 
A presumption in favor of an affirmative answer to 
these questions is suggested by the fact that the correla- 
tion between the annual rainfall in the Ohio Valley and 
the annual rainfall in the state of Illinois is r=-6.00. 
The graph of the curve of rainfall in IlUnois is given 
in Figure 7. Its equation is 

^=38.53+3.03 sin (1^ f +325° 35' V 1.87 sin^l^ ^+194° 55'") 

+3.05 sin (^/ +241° 52') +1.12 sin /y ^+232° 26' V 

the origin being at 1870. The root-mean-square devia- 

but in no year were fewer than seven records obtainable while for a 
large proportion of the years the thirty records were complete. 



Cycles of Rainfall 



29 




+ 



+ 








o 


i-H U 




+ o 




t= [CO 


!» 


Tt< 1 CO 


a 




« 


c 


p 


cc 



fo 



+ 



+ 



+ 



ssLfoui ui f/B^uiPJ /enuuy 



30 Economic Cycles: Their Law and Cause 

tion of the observations from this curve is S =4.20. In 
case of the Ohio curve the root-mean-square deviation 
was /S=5.29. But this is a better relative fit for the 
IlHnois curve than we have a right to claim, because in 
Ohio the mean annual rainfall is 41.19, while in Illinois 
the mean is 38.53. If we express the relative scatter of 
the observations about the curve as the ratio of the 
root-mean-square deviation of the observations to the 
mean rainfall, we get for Ohio and Illinois, respectively, 
Si = .128;>Si = .109. 

In Figure 8, the Ohio curve for 1870-1910 is placed 
upon the same chart as the Illinois curve for the same 
flow of time, and the degree of correspondence of the 
two curves is seen to be so close that, with due allowance 
for the difference in their mean annual rainfall, they 
seem to be almost congruent. 

We may say, therefore, that the two curves fit their 
respective data equally well. 

Our problem has now received its solution. Annual 
rainfall in the chief grain-producing area of the United 
States has no secular trend, but its mean course is the 
resultant of causes producing two cycles of 33 years 
and 8 years respectively. The manner in which these 
cycles of rainfall produce a rhythmical expansion and 
contraction in the yield of the crops we shall examine in 
the next chapter. 



Cycles of Rainfall 



31 




ssLfoui ui ii9j.uiej iPnuuY 



32 



Economic Cycles: Their Law and Cause 



APPENDIX 



TABLE I. — ^Annual Rainfall in the Ohio Valley 
Stations: Cincinnati, Portsmouth, Marietta 



Year 


Rainfali, in 
Inches 


Year 


Ratnfall in 
Inches 


Year 


Rainfall in 
Inches 


1839 


29.92 


1863 


37.95 


1887 


38.00 


1840 


42.84 


1864 


36.68 


1888 


46.19 


1841 


43.94 


1865 


48.93 


1889 


37.06 


1842 


41.89 


1866 


47.37 


1890 


55.43 


1843 


48.20 


1867 


40.72 


1891 


40.68 


1844 


37.95 


1868 


46.87 


1892 


36.96 


1845 


40.11 


1869 


41.29 


1893 


40.80 


1846 


48.39 


1870 


37.46 


1894 


31.07 


1847 


55.26 


1871 


29.91 


1895 


29.06 


1848 


44.97 


1872 


32.90 


1896 


39.22 


1849 


46.37 


1873 


45.18 


1897 


44.80 


1850 


54.77 


1874 


38.48 


1898 


45.04 


1851 


32.54 


1875 


44.78 


1899 


40.46 


1852 


46.73 


1876 


47.34 


1900 


33.60 


1853 


35.67 


1877 


34.69 


1901 


31.78 


1854 


40.30 


1878 


36.35 


1902 


39.53 


1855 


47.89 


1879 


39.22 


1903 


37.98 


1856 


28.98 


1880 


49.94 


1904 


28.24 


1857 


37.95 


1881 


41.60 


1905 


42.81 


1858 


55.48 


1882 


56.10 


1906 


41.95 


1859 


46.68 


1883 


49.25 


1907 


46.68 


1860 


36.00 


1884 


40.05 


1908 


33.29 


1861 


43.81 


1885 


37.63 


1909 


41.40 


1862 


40.26 


1886 


39.61 


1910 


36.20 



Cycles of Rainfall 



33 



TABLE II. — The Periodogram of Rainfall in the Ohio 

Valley 



y = F(t) = Ao + ai cos kt + bi sin kt = Ao -{- Ai sin (kt -f- e) 



Length 

OF 

Period 
IN Years 


a2 


62 


a2 +62=^2 


Length 
of Pe- 
riod IN 
Year8 


a2 


b- 


a'^+b^=A'- 


3 


1.2628 


2.4821 


3.7449 


21 


.0046 


4.4260 


4.4306 


4 


.0003 


4.5689 


4.5692 


22 


.2454 


2 . 4237 


2.6691 


5 


.0897 


.4520 


.5417 


23 


.8471 


.8714 


1.7185 


6 


.2220 


.1403 


.3623 


24 


.3551 


.0678 


.4229 


7 


2.1838 


3.7869 


5.9707 


25 


.2755 


. 1327 


.40S2 


8 


9.8215 


7.2563 


17.0778 


26 


.0566 


.0002 


.0568 


9 


.0327 


.3120 


.3447 


27 


.9692 


.0019 


.9711 


10 


.5978 


.0190 


.6168 


28 


.6227 


.0300 


.6527 


11 


1.0756 


.6791 


1.7547 


29 


4.2657 


1.1153 


5.3810 


12 


.4371 


.1143 


.5514 


30 


.6464 


.4767 


1.1231 


13 


.0044 


.0007 


.0051 


31 


.6112 


.5923 


1.2035 


14 


. 1078 


.1670 


.2748 


32 


.5776 


1.1168 


1 . 6944 


15 


.1874 


.0863 


.2737 


33 


2.3199 


5.9974 


8.3173 


16 


.7691 


.0424 


.8115 


34 


.2017 


1 . 7652 


1 . 9669 


17 


.9795 


.0626 


1.0421 


35 


.0456 


1.7914 


1 . 8370 


18 
19 
20 


2.9332 

1.4777 

.0294 


.9270 


3.8602 
3.4199 
1.6255 


36 


.0036 


6.8567 


6.8603 


1 . 9422 
1.5961 


Mea 


n value 


3f A' = 2.5459 



34 



Economic Cycles: Their Law and Cause 



TABLE III. — Annual Rainfall in Illinois 



Year 


Rainfall in Inches 


Year 


Rainfall in Inches 


1870 


29.65 


1891 


34.11 


1871 


36.53 


1892 


44.17 


1872 


33.98 


1893 


35.89 


1873 


41.62 


1894 


28.99 


1874 


32.91 


1895 


32.92 


1875 


40.34 


1896 


38.27 


1876 


45.50 


1897 


37.44 


1877 


42.76 


1898 


49.09 


1878 


37.61 


1899 


34.95 


1879 


36.10 


1900 


36.19 


1880 


42.31 


1901 


27.17 


1881 


42.32 


1902 


42.65 


1882 


49.04 


1903 


35.97 


1883 


47.81 


1904 


39.33 


1884 


45.83 


1905 


37.33 


1885 


40.80 


1906 


38.10 


1886 


36.16 


1907 


40.61 


1887 


33.40 


1908 


36.76 


1888 


39.41 


1909 


44.74 


1889 


36.27 


1910 


34.34 


1890 


40.34 


Mean 


38.53 



CHAPTER III 

RAINFALL AND THE CROPS 

" It is mere weather . . . doing and undoing \\ithout end." 

— William James. 

In the preceding chapter the course of annual rainfall 
in the great cereal-producing area of the United States 
has been shown to move in cycles: There is a ground- 
swell of thirty-three years in length upon which cycles 
of eight years in duration are superposed. Our object 
in studying the rhythmic changes in the volume of rain- 
fall was to bring these changes into relation with the 
variations in the yield per acre of the crops, and in the 
present chapter we shall be able to realize our purpose. 
The actual course of the varying yield per acre of the 
crops will be shown to have both a secular and a cyclical 
movement; these two movements will be separated for 
representative crops; and the cyclical movements will 
be shown to be dependent upon the cyclical movements 
in the weather represented by the cycles of rainfall. 

The Secular Trend in the Yield of the Crops 

The state of Illinois was chosen in the preceding 
chapter to illustrate the general conditions of rainfall 
in the Corn Belt of the Middle West, and we shall now 
examine the statistics of the yield of its most important 
crops. 

35 



36 Economic Cycles: Their Law and Cause 

According to the Yearbook of the Department of 
Agriculture for 1912, we find the acreage and value of 
the leading Illinois crops as they are given in the 
subjoined Table : 

Acreage and Value of Crops in Illinois, 1912 



Crop 


Acreage 


Value of Crop 


(1) Corn 


10,658,000 


$174,791,000 


(2) Oats 


4,220,000 


54,818,000 


(3) Hay 


2,512,000 


41,152,000 


(4) Wheat 


1,183,000 


8,641,000 


(5) Potatoes 


137,000 


8,302,000 


(6) Barley 


57,000 


952,000 


(7) Rye 


48,000 


538,000 


(8) Buckwheat 


4,000 


70,000 


(9) Tobacco 


900 


62,000 



It is clear, from this Table, that five crops — corn, oats, 
hay, wheat, and potatoes — make up the bulk of the 
crops of Ilhnois, and one could not go far wrong if he 
based his generalizations as to the conditions of agricul- 
ture in the state upon these five crops. But for the 
purposes we have in view, in this and other chapters, it 
is not possible to utilize the statistics of wheat produc- 
tion because both spring and winter wheat are grown in 
the state, and the statistics of their relative yield and 
price are not given in the published material for the 
long record covered in our investigation. Accordingly, 
the crops that have been actually used in our inquiry 
are corn, oats, hay, and potatoes. These crops total 
93.13 per cent, of the crop acreage and 96.45 per cent, of 
the crop value as these quantities are given in the above 
Table. 



Rainfall and the Crops 37 

As the yield per acre of the various crops may show a 
secular as well as a complex cyclical change, it will be 
necessary, before their cyclical elements can be brought 
into relation with the corresponding cyclical changes of 
rainfall, to eliminate from the recorded course of the 
yield per acre of the several crops the element of change 
that is secular in character. 

The method that has been adopted here to effect the 
elimination of the secular change is simple, but to secure 
a first approximation, it is adequate. For a period of 
time covered by the statistics, a change is regarded as a 
secular change if, for the period of time taken as a 
whole, the yield per acre of the crop shows a tendency 
either to increase or to decrease. In order to determine 
whether there is a secular change in the yield per acre, 
for a certain period of time, the yield data are correlated 
with time, and the existence or non-existence of a 
secular change is inferred from the relative magnitudes 
of the coefficient of correlation and its probable error. 
If there be a secular change, the calculation of the 
coefficient of correlation of the yield with time is then a 
first-step toward the elimination of the secular element 
by means of a regression equation in which the co- 
efficient of correlation is a factor. 

The method may be illustrated by taking the history 
of the yield per acre of corn. In Figure 9 the actual 
yield per acre in Illinois is plotted for the period 1870- 
1910. The straight fine showing the secular trend of the 
yield is the graph of the regression equation between 
the yield per acre and time. The correlation of the 



38 Economic Cycles: Their Law and Cause 




ajopjsd UJOOJ.O sjai^sng 



Rainfall and the Crops 39 

yield per acre and time is r = .382=*= .090, and the regres- 
sion equation is, ?/ = .204.t+26.93, where y= yield per 
acre, a: = time, and the origin is at 1870. The secular 
trend is eliminated by means of the facts summarized 
in the regression equation: Beginning with the year 
1870, as many times .204 are subtracted from the 
yield per acre for the several years, as the respective 
years differ from 1870. For example, the yield for the 
year 1872 was 39.8 bushels per acre; consequently the 
reduced yield for that year was 39.8-2(.204) =39.8- 
.408 =39.39. Figure 10 traces the yield per acre of corn 
freed from the secular trend. 

Of the four leading crops of Illinois that form the 
basis of our investigation, only two, corn and potatoes, 
show a significants tendency to secular change. The 
correlation between the yield per acre and time is, 
for hay, r = .013 ±.105 and, for oats, r = .043^.105; 
consequently the figures for the yield per acre of these 
two crops have not been reduced. In the case of 
potatoes, r = .122 ±.104, and the regression equation 
is ?/ = .233a: +70.51, where the origin is at 1870. The 
figures for the actual yield per acre and the reduced 
yield per acre for corn and potatoes, as well as the 
figures for the yield of hay and of oats, are given - in 
Table I of the Appendix to this chapter. 

1 The indicated secular trend in potatoes is not significant in 
the mathematical sense, because the probable error of the coefficient 
of correlation is nearly as large as the coefficient itself. I have 
nevertheless eliminated the indicated secular trend before using the 
data. 

2 The raw data were taken from Bulletins 56, 58, 62, 63 of the 



40 Economic Cycles: Their Law and Cause 



T r 



n r 



"^-"^ 


];:: 


^_J 




^^_— — -- 


- 


« 


~-~~^^ 



a 



■Ayjp ujc/ u^oo JO sfdLjsng 



Rainfall and the Crops 41 

Critical Periods Of Growth 

If the rhythmical changes in rainfall are to give the 
clue to the changes in the yield of the crops, the varia- 
tions in the rainfall must be closely related with the 
variations in the yield of the crops. But different crops 
have different times of planting and of harvesting, 
different periods of growth, and different requirements 
of moisture at the various stages of growth. The direct 
way to find whether the course of rainfall determines 
the course of the varying yield of the crops is first to 
ascertain the critical season for every crop ; and then to 
compare the course of the yield of each crop with the 
course of the rainfall of its critical season. 

The method of discovering the critical period of a 
crop may be illustrated in the treatment of corn. In 
Table II of the Appendix to this chapter, the mean ^ 
monthly rainfall for Illinois is tabulated for seven 
months, March, April, May, June, July, August, and 
September. Table I of the Appendix records the data 

Bureau of Statistics of the United States Department of Agriculture 
and from recent Yearbooks of the United States Department of 
Agricuh-ure. 

1 The raw data were taken from Bulletin W of the Wcatlier 
Bureau of the United States and from the Annual Reports of the 
Chief of the Weather Bureau. The stations used in computing the 
mean monthly rainfall were, in Northern Illinois: Aurora, Cam- 
bridge, Chicago, Tiskilwa, Galva, Kishwaukee, Ottawa, Wiimcbago 
and Henry. In Central Illinois: Charleston, Carhnville, Coatsburg, 
Decatur, Griggsville, Knoxville, Havana, LaHarpe, Pana, Peoria 
and Springfield. In Southern Illinois: Cairo, Cobden, Carlyle, 
Golconda, Flora, Greenville, McLeansboro, Mascoutah, Mt. 
Carmel and Palestine. 



42 Economic Cycles: Their Law and Cause 

referring to the yield per acre of the several crops after 
the secular trends have been eliminated. These two 
Tables furnish the statistical material for ascertaining 
the critical periods of the respective crops. The facts 
as to the times of planting and harvesting may be 
obtained from an article in the Yearbook of the United 
States Department of Agriculture, 1910, pp. 488-494, 
on ''Seedtime and Harvest: Average Dates of Planting 
and Harvesting in the United States." The method of 
detecting the period of critical relation between yield 
and rainfall consists in ascertaining, for each crop, the 
month or combination of months, within the interval 
between planting and harvesting,^ whose rainfall gives 
the highest correlation with the ultimate yield per 
acre of the crop. The time for planting corn in IlHnois, 
according to the official publication cited above, begins 
about April 30, it is general about May 13, and it ends 
about June 2. The average time for harvesting, accord- 
ing to the same pubhcation, begins about September 26, 
is general by October 29, and ends about December 10. 
The correlation between the yield of corn per acre 
(secular trend eliminated), and the rainfall for June is, 
r = .069; for July, r = .496; for August, r = .293; for 
September, r = .087; for July and August combined, 
r = .589. The critical period of growth for corn has, 
therefore, been assumed to be the interval of two 
months — July and August.^ 

' For some purposes it would be desirable to test the correlation 
beyond these limits. 

2 Of course all possible combinations of months have not been 



Rainfall and the Crops 43 

The critical periods for the other crops are, for oats — 
May, June, July, r = .290; for hay — March, April, 
May, June, r = .620; for potatoes — July and August, 
r = .666. The critical season for corn, as we found a 
while ago, is July and August, r = .589. 

The high correlation between the yield of the crops 
and the rainfall of their respective critical seasons 
promises well for the theory as to the relation of the 
cycles of rainfall and cycles of crops. In the last chapter 
we found that by examining the periodogram of annual 
rainfall in the Ohio Valley, cycles of eight years and of 
thirty-three years were discovered; and that by taking 
periods of thirty-three years and eight years with their 
semiharmonics, a good fit to the annual rainfall curve 
was obtained. It was then shown that the annual rain- 
fall in Illinois is correlated with the annual rainfall 
in the Ohio Valley, the correlation coefficient being 
r = .600. Upon the basis of this relatively high correla- 
tion, it was assumed that the annual rainfall in Illinois 
passed through similar cycles to the rainfall in the 
Ohio Valley, and we found that this assumption was 
justified by the facts inasmuch as the harmonic analysis 
applied in the same way to the Illinois data afforded as 
good a fit as when it was applied to the data of the 
Ohio Valley. Since in two of the four representative 
crops the correlation between the yield and the rainfall 

exliausted in the above case, nor have we made any attempt to 
place the critical period for a smaller inter\'al of time than a month. 
If for any other period a closer relation could be found than r = .589, 
the conclusions that we draw from our investigation would only be 
strengthened. 



44 Economic Cycles: Their Law and Cause 

of the critical season of growth is greater than the 
correlation between the annual rainfall in Ilhnois and 
the annual rainfall in the Ohio Valley, there would 
seem to be excellent ground for believing that the cycles 
of the yield of the crops would flow congruently with 
the cycles of rainfall during their respective critical 
periods. 

Cycles in the Yield of the Representative Crops and the 
Corresponding Cycles of Rainfall 

The method of bringing the cycles of rainfall for the 
critical period of growth of the several crops into rela- 
tion with the cycles of the respective crops is similar to 
the method that was employed in passing from the 
cycles of annual rainfall in the Ohio Valley to the 
corresponding cycles in the state of Illinois. The 
laborious but direct way of treating the problem would 
be to compute the periodogram of rainfall for the 
critical period of growth of each crop, and then to com- 
pare the results with the corresponding periodograms of 
the respective crops. It may be that this laborious 
process may eventually have to be followed. The 
process that has been adopted in the present investiga- 
tion makes several assumptions which it is highly 
desirable to have clear in mind. It is assumed 

(1) That the course of the annual rainfall is the mean 
course of the rainfall of the parts of the year 
and that, consequently, by computing the 
periodogram of annual rainfall, we obtain a 
general type of curve for describing not only 



Rainfall and the Crops 45 

the annual rainfall but also the rainfall of 
any considerable part of the year. Or, more 
concretely, that the annual rainfall and the 
rainfall of any considerable part of the year 
may be described by an equation of the form 

y = A^ + A^ sin (^^ t + e^j + A^ sin /^ t + e^ 
+ a^ sin i-^t + r]A + CL, sin i-^t + 172), 

where the constants in the series may be differ- 
ent for the several parts of the year. 

(2) That where the correlation between the yield per 

acre of a particular crop and the rainfall of its 
critical season is high, the same general type 
of equation will fit both groups of data, the 
data of rainfall and the data of the yield per 
acre of the crops. 

(3) That both of the preceding assumptions are 

greatly fortified if the compound curves de- 
duced from the actual data of rainfall and 
yield satisfy a reasonable test of fit to the data. 

The working out of the consequences of these as- 
sumptions is exhibited in Figures 11, 12, 13, and the 
equations descriptive of the several curves. appear on 
the corresponding Figures. 

To measure the degree of fit of the curves to their 
respective data, we shall employ a coefficient K, which 
may be described as the ratio of the arithmetical sum 
of the deviations of the observations from the curve 



46 



Economic Cycles: Their Law and Cause 



Bushels of potdtoes per acre 




■^fn^nw pup ^fnp 'saLjDui ui //pjuiey 



Rainfall and the Crops 



47 



Tons of hdy per acre 




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■»unp'/(pj^'ludY'LjOyie^ffj's3Ljoui ui /fP/^'Py 



48 



Economic Cycles: Their Law and Cause 



Bushels of corn per acre 





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Rainfall and the Crops 49 

divided by the area included between the curve and the 
straight Une indicating the mean value of the observa- 
tions. In the equation to the compound cycle describ- 
ing the typical curve with which we shall have to deal, 
the first term gives the mean value of the observations, 
and the remaining four harmonic terms trace the area 
about the horizontal line drawn at a distance from the 
base line equal to the mean value of the observations. 
The reason for adopting this complex coefficient K is 
that the curves whose relative degrees of fit are in 
question apply to qualitatively different things. From 
the method of calculating K, it follows that the smaller 
the value of K, the better is the degree of fit of the curve 
to the observations. 

Passing now to the calculations referring to the 
representative crops, we find, 

For potatoes, the correlation of the yield per acre 
with the rainfall of its critical period — July and Au- 
gust—is r = .666. The measure of the fit of the com- 
pound cycle of thirty-three years and eight years with 
their semiharmonics is, in case of the yield per acre, 
K = 1.97, and in case of the rainfall of the critical period 
of growth, K = 1.30. 

For hay, the correlation of the yield per acre with 
the rainfall of its critical period — March, April, May, 
June — is r = .620. The measure of the fit of the com- 
pound cycle to the data is, in case of the yield per acre, 
K = 1.57, and in case of the rainfall of the critical season, 
K = 1.63. 

For corn, the correlation of the yield per acre with 



60 Economic Cycles: Their Law and Cause 

the rainfall of the critical season — July and August — 
is r = .589. The measure of the fit of the compound 
cycle to the data is, for the yield per acre, i^ = 1.52, 
and, for the rainfall of the critical season, K = 1.30. 

For oats, the computation of the equation has not 
been carried out because no critical period of growth 
could be found in which the correlation between yield 
and rainfall was higher than r = .3. The correlations 
were, for March, r = — .181; for April, r=— .147; for 
May, r = 120; for June, r = .297; for July, r = .140; for 
May, June, and July, r = .290. 

Referring now to the Figures 11, 12, 13 and to the 
calculations that have just been reviewed, we observe 
that the compound cycles of yield per acre and of the 
rainfall of the critical seasons flow almost congruently, 
and that the compound cycle of thirty-three years 
and eight years with their semiharmonics fits the yield 
data nearly as well as it fits the rainfall data. 

Cycles in the Index of Crop Fluctuations and in the Cor- 
responding Index of Mean Effective Rainfall 

Does the cyclical movement of rainfall give a rhyth- 
mic movement to the fluctuations in the yield of the 
crops taken all together? The preceding section has 
treated the relation of the yield of the separate crops 
to the rainfall of their respective critical seasons; we 
now inquire whether the yield of all of the crops taken 
together shows a tendency to conform to the cychcal 
movement of rainfall. In order to answer this question 
two preliminary steps must be taken: (1) A method 



Rainfall and the Crops 51 

must be devised for measuring the fluctuation in the 
yield of the crops when the crops are taken all together; 
and (2) a method must be devised for combining the 
rainfall of the critical periods of the growth of the 
several crops. These two steps we shall now consider. 
In regard to the first of these desiderata, it is clear 
that the measure of the fluctuation of crops taken as a 
whole should be based upon the best measure of the 
fluctuation of the yield of the crops taken singly. More- 
over, there is a general agreement that the standard 
deviation of a frequency scheme is a good measure of 
the scatter of the observations about their mean value. 
A natural step, therefore, would be to assume that if 
the observations form a series in time, a good rela- 
tive measure of their fluctuations at different epochs is 
afforded by the ratio of the deviations of the observa- 
tions from their mean divided by the standard devia- 
tion. For example, the mean yield of oats in lUinois, 
for the period 1870 to 1910, was 31.4 bushels per acre, 
and the standard deviation of the yield for the same 
period of time was cr = 5.2 bushels. The yield per acre 
for the year 1910 was 38.0 bushels. If A be taken to rep- 
resent the deviation of the yield of any year from the 
mean yield of the whole period, then the A for 1910 was 
38.0 — 31.4=6.6, and the fluctuation for 1910 was 

- = —^ = 1.27. Similarly, for the year 1908, when the 
yield was 23.0 bushels, the fluctuation was, - = — 1.62. 

It happens that in the case of oats, there is no secular 
trend to the yield, but when the secular trend exists, 



52 Economic Cycles: Their Law and Cause 

it must be eliminated before the fluctuation is com- 
puted. 

In Table III of the Appendix to this chapter the 
fluctuation for each of the forty-one years 1870-1910 
is given for corn, oats, hay, and potatoes. By taking 
the algebraic sum of the fluctuations for all the crops 
for any given year and dividing by four — the number of 
the crops — a measure of the fluctuation of the crops 
taken all together is obtained. This measure we shall 
refer to as the index of the fluctuation of crops. The 
index for each of the years 1870-1910 is recorded in the 
last column of Table III. 

The index of crop fluctuation computed in the man- 
ner that has just been described is regarded as a more 
accurate measure of the fluctuation of crops than 
would be obtained from an index formed by taking as 
the fluctuation for each year, in case of each crop, the 
ratio of the deviation from the mean divided by the 
mean. If the crops differ in their coefficients of varia- 
tion, that is to say, if the ratio -^, where M is the mean 

yield and cr is the standard deviation, is not the same 

for all crops, then the crop with the largest coefficient of 

variation would receive the largest weight in the general 

index. The coefficients of variation for the crops in 

5 84 5 17 

our Table are, for corn, ^^-^ - =.217; for oats, ^r^-—. = 

ZO.Jo 1.4:4: 

.164; for hay, j^ = .137; for potatoes, ?^ = .330. If 

the usual method of forming index numbers were em- 
ployed in this case to measure crop fluctuations, the 



Rainfall and the Crops 53 

several crops would, in consequence of their different 
variabilities, receive disproportionate weights. The 
method of calculating the index which we have em- 
ployed obviates this difficulty. 

Having now obtained an index of the fluctuation of 
crops, we next consider the method of combining the rain- 
fall of the critical periods of growth for the several crops. 
The method will be clear if we bear in mind that the 
critical period of growth of a crop is the combination of 
months whose rainfall gives the highest correlation with 
the yield. The mean effective monthly rainfall for the 
critical period of a crop is the total rainfall of the critical 
period of growth divided by the number of months mak- 
ing up the critical period. In case of hay, for example, 
the critical period of growth is March, April, May, 
June. The mean effective rainfall for any given year 
would be the total rainfall for the four months, March, 
April, May, June, divided by the number of the months. 
If the mean effective monthly rainfall for the several 
crops is summed for each year and divided by the num- 
ber of crops, a measure is obtained of the mean effective 
monthly rainfall for the crops taken all together. In 
Table IV of the Appendix to this chapter the mean 
effective rainfall of the several crops, and of the crops 
taken all together, is tabulated for each of the years 
1870-1910. 

We have now an index of the fluctuation of crops and 
an index of the mean effective rainfall of the critical 
periods of the crops. The correlation between the 
two series is r = .584. In Figure 14 are traced the graphs 



54 



Economic Cycles: Their Law and Cause 



Index of f/ucfuation of crops. 




■//PJUIPJ /(fLf^UOLU 9AI4.D3jya upaf/i/ 



Rainfall and the Crops 55 

of the compound cycles that describe the two series, 
each graph consisting of two cycles and their semi- 
harmonics, a thirty-three years cycle describing the 
ground-swell and the smaller cycle of eight years sum- 
marizing the minor cyclical movements. The measure 
of the degree of fit to the observations is, in case of the 
yield curve, K = 2.46, and in case of the rainfall curve, 
K = 1.68. The yield curve reproduces the general 
characteristic features of the rainfall curve. 

Our findings with reference to the crops taken to- 
gether are similar to what we discovered in case of the 
single crops: The yield per acre and the rainfall of the 
critical season are highly correlated; the rhythmical 
movements of the yield and of the effective rainfall 
may be accurately described by a compound cycle of 
thirty-three years and eight years with their semi- 
harmonics; and the yield curve reproduces the general 
characteristics of the curve of effective rainfall. 

Passing now to a summary of the contents of this 
chapter, we may collect our results in a series of prop- 
ositions. 

(1) The yield per acre of the four representative 

crops, corn, hay, oats, and potatoes is associ- 
ated with the amount of the rainfall of their 
respective critical periods of growth. In 
three out of the four cases the degree of cor- 
relation lies between r = .589 and r = .666. 

(2) The rhythmical changes in the jdeld per acre of 

the crops and in the rainfall of the respective 



56 Economic Cycles: Their Law and Cause 

critical seasons may both be accurately de- 
scribed by a compound cycle composed of a 
thirty-three years cycle with its semihar- 
monic, which summarizes the ground-swell of 
the movement, and a superposed cycle of eight 
years with its semiharmonic, describing the 
shorter rhythmical movements. 

(3) In three of the four representative crops, the 

compound cycles summarizing the changes in 
the rainfall of the critical periods of growth 
and the changes in the yield per acre of the 
crops are so nearly congruent that, consider- 
ing the high correlation of the yield with the 
rainfall, one may conclude, with a high degree 
of probabiUty, that the rhythmical movement 
in the weather conditions represented by 
rainfall is the cause of the cycles of the crops. 

(4) The index of the fluctuation of the crops taken 

together, and the index representative of the 
mean effective rainfall during the critical 
seasons are highly correlated, r = .584. 

(5) The rhythmical changes in the index of the 

fluctuation of the crops and in the index of 
the mean effective rainfall are accurately 
described by a compound cycle which is made 
up of a thirty-three years cycle and an eight 
years cycle with their semiharmonics, and 
these two compound curves are, in their gen- 
eral characteristics, much ahke. 

(6) The investigation of the crops taken singly and 



Rainfall and the Crops 57 

taken together leads to the general conclu- 
sions : 

{a) that there is a rhythmical movement 
in both the yield of the crops and in the 
rainfall of the critical periods which is 
sunamarized in a compound cycle, in 
which the constituent elements are a 
ground-swell of thirty-three years and 
its semiharmonic, and a shorter super- 
posed cycle of eight years with its 
semiharmonic ; 
(6) that the cyclical movement in the 
weather conditions represented by rain- 
fall is the fundamental, persistent cause 
of the cycles of the crops. 



APPENDIX 



TABLE I. — The Crops of Illinois 



Year 


Yield Per Acre of 
Corn, in Bushels 


Yield Per Acre of 
Potatoes, in Bushels 


Yield Per 

Acre op 

Hav, in 

Tons 

Ton = 2000 

lbs. 


Yield Per 
Ache op 
Oats, in 
Bushels 


Actual 
Yield 


Reduced 
Yield 


Actual 
Yield 


Reduced 
Yield 


1870 


35.2 


35.2 


81 


81.0 


1.18 


26.0 


1871 


38.3 


38.1 


61 


60.8 


1.31 


33.1 


■ 1872 


39.8 


39.4 


75 


74.5 


1.35 


36.6 


1873 


21.0 


20.4 


40 


39.3 


1.25 


30.0 


1874 


18.0 


17.2 


55 


54.1 


1.20 


17.5 


1875 


34.3 


33.3 


128 


126.8 


1.37 


33.0 


1876 


25.0 


23.8 


75 


73.6 


1.40 


20.0 


1877 


29.0 


27.6 


93 


91.4 


1.60 


37.0 


1878 


27.1 


25.5 


67 


65.1 


1.49 


35.9 


1879 


35.0 


33.2 


88 


85.9 


1.21 


32.0 


1880 


27.2 


25.2 


75 


72.7 


1.45 


31.8 


1881 


19.4 


17.2 


48 


45.4 


1.30 


33.4 


1882 


23.0 


20.6 


85 


81.8 


1.25 


40.7 


1883 


25.0 


22.4 


92 


89.0 


1.45 


36.1 


1884 


30.0 


27.1 


79 


75.7 


1.40 


32.8 


1885 


31.4 


28.3 


87 


83.5 


1.30 


32.8 


1886 


24.5 


21.2 


67 


63.3 


1.34 


31.8 


1887 


19.2 


15.7 


33 


29.0 


.80 


29.5 


1888 


35.7 


32.0 


80 


75.8 


1.40 


35.8 


1889 


32.3 


28.4 


99 


94.6 


1.39 


37.5 


1890 


26.2 


22.1 


30 


25.3 


1.30 


21.0 


1891 


33.5 


29.2 


92 


87.1 


1.25 


34.0 


1892 


26.2 


21.7 


52 


46.9 


1.25 


26.3 


1893 


25.7 


21.0 


53 


47.6 


1.21 


27.2 


1894 


28.8 


23.9 


50 


44.4 


1.14 


36.1 


1895 


37.4 


32.3 


77 


71.2 


.66 


24.4 


1896 


40.5 


35.2 


97 


90.9 


1.38 


28.0 


1897 


32.5 


27.0 


38 


31.7 


1.29 


32.0 


1898 


30.0 


24.3 


70 


63.5 


1.56 


29.0 


1899 


36.0 


30.1 


96 


89.2 


1.29 


38.0 


1900 


37.0 


30.9 


90 


83.0 


1.27 


38.0 


1901 


21.4 


15.1 


35 


27.8 


1.08 


28.2 


1902 


38.7 


32.2 


118 


110.5 


1.50 


37.7 


1903 


32.2 


25.5 


72 


64.3 


1.54 


26.6 


1904 


36.5 


29.6 


108 


100.1 


1.36 


32.0 


1905 


39.8 


32.7 


75 


66.8 


1.35 


35.5 


1906 


36.1 


28.8 


97 


88.6 


.98 


29.5 


1907 


36.0 


28.4 


87 


78.4 


1.40 


24.5 


1908 


31.6 


23.8 


71 


62.2 


1.53 


23.0 


1909 


35.9 


27.9 


91 


81.9 


1.45 


36.6 


1910 


39.1 


30.9 


75 


65.7 


1.33 


38.0 



58 



Rainfall and the Crops 



59 



TABLE II. — Mean Monthly Rainfall in Illinois 





Mean Mo.nthly Rainfall 


Year 


March 


April 


Mat 


June 


July 


August 


Septem- 

BEB 


1870 


3.92 


1.43 


1,64 


1.93 


2.85 


3.95 


3.69 


1871 


3.31 


2.47 


3.06 


4.00 


3.11 


3.50 


1.22 


1872 


2.59 


3.39 


3.60 


5.68 


5.00 


3.65 


4.29 


1873 


1.75 


4.98 


4.87 


2.18 


3.99 


1.77 


3.19 


1874 


2.39 


3.50 


2.25 


3.45 


2.06 


4.28 


3.95 


1875 


2.83 


2.60 


4.57 


5.36 


9.37 


1.96 


4.60 


1876 


5.13 


3.38 


4.68 


5.53 


4.91 


3.83 


4.33 


1877 


4.02 


3.53 


3.13 


7.39 


3.27 


2.78 


2.29 


1878 


3.04 


4.66 


5.04 


2.72 


3.83 


4.10 


1.61 


1879 


2.59 


2.42 


2.10 


4.33 


3.44 


4.89 


1.48 


1880 


3.31 


4.29 


5.93 


3.53 


3.10 


3.65 


3.59 


1881 


3.16 


2.18 


2.26 


5.93 


2.58 


0.84 


4.04 


1882 


4.00 


4.00 


6.60 


6.61 


3.46 


4.65 


2.08 


1883 


1.81 


4.16 


5.38 


5.51 


4.86 


1.86 


0.88 


1884 


3.31 


3.36 


4.40 


5.13 


4.09 


2.40 


4.80 


1885 


0.53 


4.13 


3.03 


5.63 


2.80 


5.06 


5.67 


1886 


3.02 


3.60 


4.07 


4.42 


1.15 


3.86 


4.81 


1887 


2.37 


2.46 


2.90 


1.94 


2.40 


2.46 


3.25 


1888 


4.09 


1.94 


5.18 


4.80 


3.83 


4.31 


1.46 


1889 


1.62 


2.00 


5.11 


5.35 


4.45 


1.22 


3.78 


1890 


4.34 


3.75 


3.86 


4.58 


2.03 


2.96 


3.04 


1891 


3.43 


2.91 


2.19 


4.11 


1.88 


4.71 


1.02 


1892 


2.17 


6.43 


8.06 


5.77 


3.71 


3.03 


2.01 


1893 


3.31 


7.64 


4.24 


3.51 


2.20 


0.96 


3.09 


1894 


2.98 


2.73 


3.29 


2.31 


1.58 


1.74 


4.53 


1895 


1.72 


2.17 


2.34 


2.68 


6.01 


2.76 


3.00 


1896 


1.90 


2.84 


6.09 


4.14 


6.17 


2.95 


5.79 


1897 


6.22 


4.53 


1.94 


4.28 


3.59 


1.19 


0.99 


1898 


7.70 


3.47 


6.26 


4.71 


2.84 


4.70 


5.07 


1899 


3.19 


1.64 


6.41 


3.00 


3.42 


2.70 


2.23 


1900 


2.12 


1.64 


4.51 


4.31 


4.15 


3.72 


3.59 


1901 


3.80 


1.84 


1.86 


3.55 


2.63 


1.91 


1.97 


1902 


3.64 


2.55 


3.78 


7.77 


4.78 


4.67 


4.24 


1903 


3.23 


4.51 


3.25 


3.03 


3.41 


4.58 


3.85 


1904 


6.41 


3.76 


3.29 


3.28 


5.23 


4.25 


5.43 


1905 


2.32 


3.88 


4.27 


3.69 


4.78 


3.41 


2.89 


1906 


4.09 


2.09 


2.39 


3.08 


2.58 


4.15 


5.15 


1907 


3.26 


2.89 


3.95 


4.17 


5.39 


5.56 


2.38 


1908 


3.21 


4.59 


8.07 


3.14 


3.32 


2.39 


1.41 


1909 


2.62 


5.94 


4.23 


4.04 


4.96 


2.12 


4.25 


1910 


0.32 


3.66 


5,04 


2.62 


4.72 


2.51 


4.61 



60 



Economic Cycles: 7^ heir Law and Cause 



TABLE III. — Index of Fluctuation of Crops. A — Devia- 
tion FROM THE Mean after the Secular Trend has been 
Eliminated. (^ = Standard Deviation 





Corn 


Oats 


Hat 


Pota- 


Sum op 


Sum op 




Index 

OF 


Year 


A 


A 


A 


toes 

A 


Positive 


Negative 


Differ- 


Fluct- 








Fluctua- 


Fluctua- 


ence 


uation 




a 


a 


<r 


ff 


tions 


tions 




OF 


1870 
















Crops 


1.43 


—1.04 


— .72 


.45 


1.88 


1.76 


+ .12 


+ .03 


1871 


1.93 


.33 


.00 


— .42 


2.26 


.42 


+ 1.84 


+ .46 


1872 


2.16 


1.00 


.22 


.17 


3.55 


.00 


+3.55 


+ .89 


1873 


—1.12 


— .27 


— .33 


—1.34 


.00 


3.06 


—3.06 


— .76 


1874 


—1.67 


—2.67 


— .61 


— .70 


.00 


5.65 


—5.65 


—1.41 


1875 


1.10 


.31 


.33 


2.42 


4.16 


.00 


+4.16 


+ 1.04 


1876 


— .67 


—2.19 


.50 


.13 


.63 


2.86 


—2.23 


— .56 


1877 


.12 


1.08 


1.61 


.90 


3.71 


.00 


+3.71 


+ .93 


1878 


— .24 


.87 


1.00 


— .23 


1.87 


.47 


+ 1.40 


+ .35 


1879 


1.09 


.12 


— .56 


.66 


1.87 


.56 


+ 1.31 


+ .33 


1880 


— .29 


.08 


.78 


.09 


.95 


.29 


+ .66 


+ .16 


1881 


—1.69 


.38 


— .06 


—1.08 


.38 


2.83 


—2.45 


— .61 


1882 


—1.09 


1.79 


— .33 


.48 


2.27 


1.42 


+ .85 


+ .21 


1883 


— .78 


.90 


.78 


.79 


2.47 


.78 


+ 1.69 


+ .42 


1884 


.03 


.27 


.50 


.22 


1.02 


.00 


+ 1.02 


+ .25 


1885 


.24 


.27 


— .06 


.56 


1.07 


.06 


+ 1.01 


+ .25 


1886 


— .98 


.08 


.17 


— .31 


.25 


1.29 


—1.04 


— .26 


1887 


—1.93 


— .37 


—2.83 


—1.78 


.00 


6.91 


—6.91 


—1.73 


1888 


.88 


.85 


.50 


.23 


2.46 


.00 


+2.46 


+ .61 


1889 


.26 


1.17 


.44 


1.03 


2.90 


.00 


+2.90 


+ .72 


1890 


—1.00 


—2.00 


— .06 


—1.94 


.00 


5.00 


—5.00 


—1.25 


1891 


.40 


.50 


— .33 


.71 


1.61 


.33 


+ 1.28 


+ .32 


1892 


— .90 


— .98 


— .33 


—1.01 


.00 


3.22 


—3.22 


— .80 


1893 


—1.02 


— .81 


— .56 


— .98 


.00 


3.37 


—3.37 


— .84 


1894 


— .52 


.90 


— .94 


—1.12 


.90 


2.58 


—1.68 


— .42 


1895 


.93 


—1,35 


—3.61 


.03 


.96 


4.96 


—4.00 


—1.00 


1896 


1.43 


— .65 


.39 


.88 


2.70 


.65 


+2.05 


+ .51 


1897 


.02 


.12 


— .11 


—1.67 


.14 


1.78 


—1.64 


— .41 


1898 


— .45 


— .46 


1.39 


— .30 


1.39 


1.21 


+ .18 


+ .05 


1899 


.55 


1.27 


— .11 


.80 


2.62 


.11 


+2.51 


+ .63 


1900 


.69 


1.27 


— .22 


.54 


2.50 


.22- 


+2.28 


+ .57 


1901 


—2.03 


— .62 


—1.28 


—1.83 


.00 


5.76 


—5.76 


—1.44 


1902 


.91 


1.21 


1.06 


1.72 


4.90 


.00 


+4.90 


+ 1.22 


1903 


— .24 


— .92 


1.2S 


— .27 


1.28 


1.43 


— .15 


— .04 


1901 


.47 


.12 


.2S 


1.27 


2.14 


.00 


+2.14 


+ .54 


1905 


1.00 


.79 


.22 


— .16 


2.01 


.16 


+ 1.85 


+ .46 


1906 


.31 


— .37 


—1.83 


.78 


1.09 


2.20 


—1.11 


— .28 


1907 


.26 


—1.33 


.50 


.34 


1.10 


1.33 


— .23 


— .06 


1908 


— .53 


—1.62 


1.22 


— .36 


1.22 


2.51 


—1.29 


— .32 


1909 


.17 


1.00 


.78 


.49 


2.44 


.00 


+2.44 


+ .61 


1910 


.69 


1.27 


.11 


— .21 


2.07 


.21 


+ 1.86 


+ .46 



Rainfall and the Crops 



61 



TABLE IV. — Mean Effective Monthly Rainfall in Illinois 





Mean Effective Monthly Rainfall 


Mean 
Effective 
Monthly 
Rainfall 
FOR Crops 


Year 


For 
Corn 


For 
Oats 


For 
Hay 


For 
Potatoes 


Sum of 
Preceding 
Columns 


1870 


3.40 


2.14 


2.23 


3.40 


11.17 


2.79 


1871 


3.30 


3.39 


3.21 


3.30 


13.20 


3.30 


1872 


4.33 


4.76 


3.81 


4.33 


17.23 


4.31 


1873 


2.88 


3.68 


3.45 


2.88 


12.89 


3 . 22 


1874 


3.17 


2.59 


2.90 


3.17 


1 1 . 83 


2.96 


1875 


5.66 


6.43 


3.84 


5.66 


21.59 


5.40 


1876 


4.37 


5.04 


4.68 


4.37 


18.46 


4.61 


1877 


3.02 


4.60 


4.52 


3.02 


15.16 


3.79 


1878 


3.96 


3.86 


3.86 


3.96 


15.64 


3,91 


1879 


4.16 


3.29 


2.86 


4.16 


14.47 


3.62 


ISSO 


3.37 


4.19 


4.26 


3.37 


15. '9 


3.80 


1881 


1.71 


3.58 


3.38 


1.71 


10.38 


2.59 


1882 


4.05 


5.56 


5.30 


4.05 


18.96 


4.74 


1883 


3.36 


5.25 


4.20 


3.36 


16.17 


4.04 


1884 


3.25 


4.54 


4.05 


3.25 


15.09 


3.77 


1885 


3.93 


3.82 


3.33 


3.93 


15.01 


3.75 


1886 


2.51 


3.21 


3.78 


2.51 


12.01 


3.00 


1887 


2.43 


2.41 


2.42 


2.43 


9.69 


2.42 


1888 


4.07 


4.60 


4.00 


4.07 


16.74 


4.18 


1889 


2.84 


4.97 


3.52 


2.84 


14.17 


3.54 


1890 


2.50 


3.49 


4.13 


2.50 


12.62 


3.15 


1891 


3.29 


2.73 


3.16 


3.29 


12.47 


3.12 


1892 


3.37 


5.85 


5.61 


3.37 


18.20 


4.55 


1893 


1.58 


3.32 


4.67 


1.58 


11.15 


2.79 


1894 


1.66 


2.39 


2.83 


1.66 


8.54 


2.14 


1895 


4.38 


3.68 


2.23 


4.38 


14.67 


3.67 


1896 


4.56 


5.47 


3.74 


4.56 


18.33 


4.58 


1897 


2.39 


3.27 


4.24 


2.39 


12.29 


3.07 


1898 


3.77 


4.60 


5.53 


3.77 


17.67 


4.42 


1899 


3.06 


4.28 


3.56 


3.06 


13.96 


3.49 


1900 


3.93 


4.32 


3.15 


3.93 


15.33 


3.83 


1901 


2.27 


2.68 


2.76 


2.27 


9.98 


2.50 


1902 


4.72 


5.44 


4.43 


4.72 


19.31 


4.83 


1903 


4.00 


3.23 


3.50 


4.00 


14.73 


3.68 


1904 


4.74 


3.93 


4.18 


4.74 


17.59 


4.40 


1905 


4.09 


4.25 


3.54 


4.09 


15.97 


3.99 


1906 


3.36 


2.68 


2.91 


3.36 


12.31 


3.08 


1907 


5.47 


4.50 


3.57 


5.47 


19.01 


4.75 


1908 


2.85 


4.84 


4.75 


2.85 


15.29 


3.82 


1909 


3.54 


4.41 


4.22 


3.54 


15.71 


3.93 


1910 


3.61 


4.13 


2.91 


3.61 


14.26 


3.56 



CHAPTER IV 

THE LAW OF DEMAND 

Kann man nicht die Nachfragefunktion genauer feststellen, so 
genau, dass wir nicht bloss ein eindeutiges, sondern ein konkretes 
Resultat gewinnen? Ich glaube die Antwort zu horen: Welch' 
ein phantastisches Unterfangen-Unberechenbarkeit der wirtschaft- 
lichen Vorgange — steter Wechsel — u. s. w! 

Joseph Schumpeter. 

Questions affecting for the most part the supply of 
commodities have thus far been the object of our in- 
vestigation, but the inquiry as to the cause and law of 
economic cycles must extend to a consideration of 
cycles of values and prices. Since the rhythmical 
variation in the supply of crops produces its effect upon 
crop prices in accordance with the laws of demand for 
the several crops, the obvious first and necessary step 
in bringing the results of the preceding chapters to bear 
upon the question of the cause and law of economic 
cycles is to solve the problem of the relation between 
the variations in the supply of the several crops and 
the resulting variations in their respective prices. It 
is required to derive from existing data the concrete 
laws of demand for the representative crops. 

The Theory of Demand 

The mathematical treatment of the theory of demand 
furnishes two doctrines that are of importance in our 

62 



The Law of Demand 



63 



subsequent work : The doctrine of the uniformity of the 
demand function and the doctrine of the elasticity of 
demand. The exposition of these two doctrines will be 
facilitated by reference to Figure 15, in which, accord- 
ing to the usual practice, quantities of commodity are 
measured upon the axis 
of abscissas, and the cor- 
responding prices per 
unit, upon the axis of 
ordinates. 

The doctrine of the 
uniformity of the demand 
function, which is trace- 
able to Cournot,^ but is 
especially stressed by 
Professor Marshall, has been put in these words: 
"There is then one general law of demand viz., that 
the greater the amount to be sold, the smaller will 
be the price at which it will find purchasers ; or, in other 
words, that the amount demanded increases with a 
fall in price and diminishes with a rise in price." Re- 




FiGURE 15. The law of demand. 



^ Cournot: Recherches sur les princi'pes mathimatiques de la Iheorie 
des richesses, §§ 21, 22. Assuming that the relation between price 
and the amount demanded is represented by F(p), he says, p. 54: 
"Si la fonction F(p) est continue, elle jouira de la propriety commune 
a toutes les fonctions de cette nature, et sur laquelle reposent tant 
d'applications importantes de I'analyse math6matique: les varia- 
tions de la demande seront sensiblement proportionelles aux varia- 
tions du prix, tant que celles-ci seront de petites fractions du prix 
originaire. D'ailleurs, ces variations seront de signes contraires, 
c'est-a-dire qu'^ une augmentation de prix correspondra une dimi" 
nution de la demande." 



64 Economic Cycles: Their Law and Cause 

f erring to Figure 15, this statement means that if at 
any point in the demand curve DD' , say the point P, 
a straight hne is drawn tangent to the curve, then the 
trigonometric tangent of the angle which the Hne makes 
with the positive direction of the axis of x, is negative. 
In Professor Marshall's words: ''The one universal 
rule to which the demand curve conforms is that it is 
inclined negatively throughout the whole of its length."^ 
As we proceed we shall find that the law of demand for 
some commodities does indeed conform to the type of 
curve which has just been described, but it will be a part 
of the work of the next chapter to show that the doc- 
trine of the uniformity of the demand function is an 
idol of the static state — of the method of cceteris 
paribus — which has stood in the way of the successful 
treatment of concrete dynamic problems. 

Assuming that the law of demand for a given com- 
modity is represented by the descending curve DD' in 
Figure 15, the elasticity of demand for the commodity 
when OM units are bought is measured by the ratio 

UW "^ PM '^^^^ ^^ ^^ ^^yy "^ general terms, if the price 
of the commodity undergoes a small change, the amount 
of the commodity that is demanded likewise undergoes 
a small change, and the degree of the elasticity of de- 
mand for the commodity, in the given state of the mar- 
ket, is measured by the ratio of the relative change in 

^ Marshall: Principles of Economics, 4th edit., pp. 174, 174 note 2. 
In the subsequent reasoning we shall call this tj'pe of demand 
curve the negative type. 



The Law of Demand 65 

the amount demanded to the small relative change in 
the price. Or, more definitely, if ''a fall of 1 per cent, 
in price would cause an increase of 2 per cent, in the 
amount demanded, the elasticity of demand would be 
two;" if ''a fall of 1 per cent, in price would cause an 
increase of Va P^r cent, in the amount demanded, the 
elasticity of demand would be one-third; and so on." ^ 
It will be observed that the theory of elasticity of 
demand in this classical form is presented from the 
point of view of infinitesimal changes in the two va- 
riables — , price and commodity demanded. It gives 
the degree of elasticity of demand for a point in time, 
for a given state of the market assuming all other 
things to remain the same ; and for this reason it may be 
said to treat of elasticity of demand from a statical 
point of view. But this is not its most serious limitation. 
It postulates a knowledge of the demand curve, and 
while it gives an exposition of the method by which the 
degree of elasticity of demand might be determined 
provided the demand curve were known, there have 
been grave doubts as to whether the practical difficulty 
of deriving the demand curve would ever be overcome. 

The problem before us is to derive the demand curve 
from statistics; to measure the degree in which it is an 
accurate description of the changes of actual industry; 
and to give the numerical coefficients of elasticity of 
demand for typical commodities. 

1 Marshall: Principles of Economics, 4th edit., pp. 177-178, 
note. 



66 Economic Cycles: Their Law and Cause 

Statistical Laws of Demand 

Two fundamental defects in the current theoretical 
method of treating economic questions are exemplified 
in the case of the theory of demand: first, the assump- 
tion is made that all other things being equal (the old 
cceteris paribus), an increase in the supply of the com- 
modity will lead to a corresponding fall in the price; 
secondly, it is assumed that the concrete problem of 
the relation of price and supply of commodity will be 
simplified by attacking first the constituent elements 
of the question rather than by attacking directly the 
problem in its full concreteness. Neither assumption 
is satisfactory nor indeed admissible. The "other 
things" that are supposed to remain equal are seldom 
mentioned and are never completely enumerated; and 
consequently the assumption that, other unmentioned 
and unenumerated factors remaining constant, the law 
of demand will be of a certain type, is really tantamount 
to saying that under conditions which are unanalyzed 
and unknown, the law of demand will take the supposed 
definite form. The burden of proof is upon anyone 
using this method to show that the assumption does not 
at least involve a physical impossibility. 

The second of the above two assumptions is not more 
satisfactory than the first. It reproduces the defects 
of the first assumption with others superadded. The 
movement of prices results from changes in many 
factors: According to the statical method, the method 
of ceteris paribus, the proper course to follow in the 



The Law of Demand 67 

explanation of the phenomenon is to investigate in 
turn, theoretically, the effect upon price of each factor, 
coBteris paribus, and then finally to make a synthesis! 
But if in case of the relation of each factor to price the 
assumption cceteris paribus involves large and at least 
questionable hypotheses, does one not completely lose 
himself in a maze of implicit hypotheses when he speaks 
of a final synthesis of the several effects? We shall not 
adopt this bewildering method, but shall follow the 
opposite course and attack the problem of the relation 
of prices and supply in its full concreteness. 

The fruitfulness of the statistical theory of correlation 
stands in significant contrast to the vast barrenness of 
the method that has just been described, and the two 
methods follow opposed courses in deahng with a 
problem of multiple effects. Take, for example, the 
question of the effects of weather upon crops. ^Vhat a 
useless bit of speculation it would be to try to solve, in a 
hypothetical way, the question as to the effect of rain- 
fall upon the crops, other unenumerated elements of 
weather remaining constant? The question as to the 
effect of temperature, cceteris paribus? How, finally, 
would a synthesis be made of the several individual 
effects? The statistical method of multiple correlation 
formulates no such vain questions. It inquires, di- 
rectly, what is the relation between crop and rainfall, 
not cceteris paribus, but other things changing accord- 
ing to their natural order; what is the relation between 
crop and temperature, other things conforming to the 
observed changes in temperature; and, finally, what is 



68 Economic Cycles: Their Law and Cause 

the relation between crop and rainfall for constant 
values of temperature? The problem of the effects of 
the constituent factors is solved only after the more 
general problem has received its solution. This method 
offers promise of an answer to the question as to the 
relation between the effective demand price and the 
supply of the commodity. 

The chief difficulties in the computation of statistical 
laws of demand are due to changes that occur in the 
market during the period to which the statistics of 
prices and of quantities of commodities refer. In order 
that the statistical laws of demand shall have sufficient 
validity to serve as prediction formulae, the observations 
must be numerous ; and in order to obtain the requisite 
number of observations, a considerable period must be 
covered. This usually means that, during the interval 
surveyed in the statistical series, important changes 
occur in the condition of the market. But in case 
of staple commodities, such as the agricultural products 
with which we shall have to deal, the effects of those 
changes in the condition of the market that obscure the 
relation between prices and amounts of commodity may 
be largely eliminated. As far as the law of demand is 
concerned, the principal dynamic effects that need to 
be considered are changes in the volume of the com- 
modity that arise from the increasing population, and 
changes in the level of prices which are the combined 
result of causes specifically responsible for price cycles 
and of causes that produce a secular trend in prices. 



The Law of Demand 69 

The effects of these two fundamental changes may be 
eUminated approximately by a single statistical device, 
namely, by deducing the law of demand from a gen- 
eralized treatment of the elasticity of demand. 

The degree of elasticity of demand, according to the 
classic formula, is measured by the ratio of the relative 
change in the amount of the conmiodity that is bought 
to the relative change in the price per unit of the com- 
modity. Suppose, now, that instead of restricting 
this conception to infinitesimal changes in price and in 
amount of commodity, we extend it to the finite changes 
that actually occur in the market. Then, the relative 
change in the amount of commodity that is bought 
may be correlated with the relative change in the 
corresponding price, and the resulting appropriate 
regression equation will give the statistical law of 
demand for the commodity. By taking the relative 
change in the amount of the commodity that is de- 
manded, instead of the absolute quantities, the effects 
of increasing population are approximately eliminated; 
and by taking the relative change in the corresponding 
prices instead of the corresponding absolute prices, the 
errors due to a fluctuating general price level are par- 
tially removed. If the observations should cover the 
period of a major cycle of prices, and the commodity 
under investigation should be a staple commodity such 
as the representative agricultural products with which 
we shall have to deal, the above method of deriving the 
demand curve will give an extremely accurate formula 
summarizing the relation between variations in price 



70 Economic Cycles: Their Law and Cause 

and variations in the amount of the commodity that is 
demanded. 

The method msiy be illustrated bj' deriving the law of 
demand for corn. In Table I of the Appendix to this 
chapter are recorded, for the period of 1866-1911, in the 
United States, the quantities of corn annually pro- 
duced, the corresponding prices per bushel, the relative 
changes in the quantity produced and the relative 
changes in the price per bushel. If the correlation of 
the relative change in the amount of corn that is pro- 
duced and the relative change in the corresponding 
price per bushel of corn is assumed to be Hnear, the 
coefficient of correlation is r = — .789, and the equation 
of regression is i/ = — .8896.T+7.79, the origin being at 
{o,o). (See Figure 16.) 

In Tables ^ II, III, lY, of the Appendix to this 
chapter, similar data are given for hay, oats, and 
potatoes. The coefficients of correlation are, for 
hay, r = —.715; for oats, r = —.722; and for potatoes, 
r — — .856. The regression equations are, 

for hay, 7/ = —. 7643a: +3.61; 
for oats, ?/ = — 1.0455^+6.93; 
for potatoes, ?/ = — 1.2194j: + 15.75; 

the origin in all cases being at (0,0). 

The high coefficients of correlation that have just 

been given were obtained on the assumption that the 

correlation between relative change in amount de- 

1 The data of the Tables I, II, Til, IV were taken from the Year- 
book of the Department of Agriculture of the United States, for 
1911. 



The Law of Demand 



71 




Percentage chande in the production of corn. 

Figure 16. The law of demand for corn. 
y = -.SS96.C + 7.79, origin at (0, 0). 



72 Economic Cycles: Their Law and Cause 

manded and relative change in price is linear. We shall 
see later on that the two variables are even more 
intimately associated than would be suggested by the 
high coefficients of correlation. Just now we wish to 
know the form of the law of demand when the restric- 
tion involved in the assumption of linearity of regres- 
sion is removed. What will be the statistical laws of 
demand for the representative commodities corn, hay, 
oats, and potatoes, if the regression of relative change in 
price upon relative change in quantity of commodity is 
assumed to be skew and of the type y =a+bx-\-cx'^-{-dx^'! 
The question is answered by fitting, according to the 
Method of Least Squares, the equation y=a+bx+cx^ + 
dx^ to the data of Tables I, II, III, IV of the Appendix 
to this chapter. The results of the computations are 
exhibited in Figures 17, 18, 19, 20 of the text. 

The statistical laws of demand for the commodities 
corn, hay, oats, and potatoes present the fundamental 
characteristic which, in the classical treatment of de- 
mand, has been assumed to belong to all demand 
curves, namely, they are all negatively inchned ; that is 
to say, speaking from the point of view of average 
results, ''the greater the amount to be sold, the smaller 
will be the price at which it will find purchasers, or, in 
other words, . . . the amount demanded increases 
with a fall in price and diminishes with a rise in price." ^ 

1 Marshall: Principles of Economics, 4th edit., p. 174. In case of 
the law of demand for hay, there is a slight upward turn at the ex- 
tremity of the curve. This is due to one extreme observation, and 
the variation is not a significant exception to the above general rule. 



The Law of Demand 



73 




Percenfade chande in the production of corn. 



Figure 17. The law of demand for corn. 
2/ = .94 — 1.0899X + .02391a;2 — .000234x3, origin at (0, 0). 



74 



Economic Cycles: Their Law and Cause 




Percenfade chande in the production of hay. 

Figure 18. The law of demand for hay. 
y = 4.17 — M60x — .00770a;2 + .OOOSSSx', origin at (0, 0). 



The Law of Demand 



76 




Perce nfaOe chonde in the production of oats. 

Figure 19. The law of demand for oats. 
y = 8.22 — 1.1904X — .00663x» + .000273xS origin at {0, 0). 



76 



Economic Cycles: Their Law and Cause 




Percentade chende in the production of potatoes. 

Figure 20. The law of demand for potatoes. 
y = 1.77 — 1.5062a; + .02489x2 — .000197a;', origin at (0, 0). 



The Law of Demand TJ 

But unlike the classical theory of demand which was 
limited to the simple enunciation of this one character- 
istic, coeteris paribus, the statistical laws that have just 
been derived apply to the average changes that society 
is actually undergoing. They summarize the changes 
in prices that are to be expected from changes in the 
supply of the commodity, thus enabling one to predict 
the probable variation in price that will follow upon an 
assigned variation in the amount of the commodity. 
They exhibit the connection of probable results not 
only in a qualitative but also in a quantitative form. 

The Prediction of Prices 

It has been said that the statistical laws of demand 
enable the economist to predict the probable variation 
in price that will follow upon an assigned variation in 
the quantity of commodity that is to be sold. How 
accurate are the results of prediction that are based 
upon the statistical law of demand? 

The accuracy of the prediction in the case of any 
given commodity will vary according to the degree of 
fit of the type of curve that is assumed to represent the 
relation between the relative change in price and the 
relative change in the quantity of the commodity. If, 
for example, the commodity in question is corn in the 
United States, and the type of demand curve is assumed 
to be linear, then, according to the results in foregoing 
pages, the correlation between the two variables is 
r= — .789, and the regression equation is ?/ = — .8896a: 
+7.79, the origin being at {o,o). (Figure 16 will facih- 



78 Economic Cycles: Their Law and Cause 

tate the discussion of the case.) By means of this law 
of demand it is possible to predict the probable change 
in the price that will follow upon a given change in 
the quantity to be sold. In 1911, in the United States, 
the quantity of corn produced was 2,531,488,000 
bushels, and the mean farm price on December 1, 1911 
was 61.8 cents. In 1912 the quantity of corn produced 
was 3,124,746,000 bushels; what, then, was the probable 
price of corn on December 1, 1912? The percentage 
change in the quantity produced was 23.44. Sub- 
stitute this value for x in the formula for the law of 
demand y= — .8896x+7.79, and solve for the value 
oiy. It is found that the probable change in price would 
be a fall of 13.06 per cent., which, since the price in 
1911 was 61.8 cents, would give 52.7 cents as the prob- 
able price for December 1, 1912, whereas the actual 
price was 48.7 cents. 

According to the theory of linear correlation, the 
accuracy of the regression equation as a prediction 
formula is measured by *S = o'j, V 1 — r^, where r is 
the coefficient of correlation between the variables, 
^y is the standard deviation of the variable y about 
its mean value, and S is the root-mean-square devia- 
tion of the actual observations about the regression 
line; or, in other words, S^ is the mean value of the 
mean-square deviations about the regression line, of 
the observations in the several arrays of y's. From 
the Table of the Probability Integral it is known 
that in a symmetrical distribution of observations 
about their mean value, 68 per cent, of all the observa- 



The Law of Demand 79 

tions fall within =*= the root-mean-square deviation of 
the observations from their mean value; 95 per cent., 
between ± twice the root-mean-square deviation; and 
99.7 per cent, between ± three times the root-mean- 
square deviation. It is therefore possible, by means 
of the Probability Integral, to affix the degree of prob- 
ability that a deviation shall fall within any given 
multiples or submultiples of the root-mean-square 
deviation. In case of the use of the Unear law of de- 
mand for corn in the United States as a prediction 
formula, the root-mean-square deviation of the ob- 
servations about the demand curve was S = ^y'^l — r^ = 
15.92 per cent. That is to say, if we assume the law of 
demand that was based upon observations from 1866 
to 1911 to hold in 1912, then it is 95 to 5, or 19 to 1, that 
the percentage variation in the actual price for 1912 
from the percentage variation as calculated from the 
law of demand will be between ± 2 (15.92), or 31.84 
per cent. The calculated percentage change in the 
price for 1912 was a fall of 13.06 per cent.; the actual 
fall was 21.20 per cent., giving a difference of 7.14 per 
cent. 

The precision with which the linear law of demand 
may be used for the prediction of the price of corn in 
the United States justifies the belief that for some pur- 
poses it is unnecessary to seek a greater degree of 
accuracy than is afforded by the simple linear laws. 
But it is well to be able to reach the maximum degree 
of precision, and for this reason we have fitted, to the 
data of the Tables in the Appendix, the more complex 



80 



Economic Cycles: Their Law a7id Cause 



curves y =a-\-bx-\-cx--\-dx^, the graphs of which, in case 
of the representative commodities corn, hay, oats, and 
potatoes, are given in Figm-cs 17, 18, 19, 20. What is 
the gain in precision when the more complex curve is 
substituted for the simple straight line? The scatter 
of the observations about the straight line of regression 
was measured, a while ago, by taking the root-mean- 
square deviation of the observations about the line, 
that is, by using S = o'y'^l—r^. In order to compare 
with this result the distribution of the observations 
about the more complex curve, y =a+bx-\-cx^+dx^, 
the distribution about the latter curve will likewise be 
measured by the root-mean-square deviation of the 
observations. In the little table given below, the 
measures of scatter of the observations for the two 
types of demand curves are presented in a form that 
will make comparison easy. 



Scatter of Observations About the Law of Demand 
Root-Mean-Square Deviation of Observations 



Crops 


When the regres- 
sion is linear 


When the regres- 
sion is skew 


Corn 

Hay 


15 . 92 per cent. 
9.53 " " 
16.02 " " 
21.29 " " 


7 . 36 per cent. 
4.65 " " 
10.17 " " 
9.94 " " 


Oats 

Potatoes 



It is clear that in all cases a gain in precision is ob- 
tained by using the more complex curve. 
Before leaving this topic a remark should be made 



The Law of Demand 81 

that has a bearing upon the a priori theory of demand. 
In treatises on pure economics, particularly in those in 
which mathematical analysis is employed, the masters 
of the a -priori method point out what they regard as 
the extreme difficulty of the actual problem of the rela- 
tion of price to quantity of commodity — a difficulty 
growing out of the interrelation of the many factors in 
the problem. If, to limit the illustration to a simple 
case, one wishes to know how the price of corn is re- 
lated to the quantity of corn that is produced, he is 
told that the problem is inextricably complex: If there 
is a deficiency in corn, then hay, or potatoes, or oats, 
or all three may be substituted in part for corn, and con- 
sequently the variation in the price of corn that fol- 
lows upon a deficiency of corn cannot be traced with- 
out knowing in what degree, when the price of corn 
varies, hay, oats, and potatoes are used as substitutes. 
But this is not all. The degree in which hay, oats, and 
potatoes are substituted for corn is dependent not only 
upon the price of corn but also on their own several 
prices, and these latter prices are, in turn, dependent 
upon the supply and price of corn! This statement of 
the problem, complex as it appears, is unduly simpli- 
fied; and it is presented not in order to ridicule the work 
of the masters who have elaborated the method of 
stating the problem in the form of simultaneous equa- 
tions, but to show how hopelessly remote from reality 
is the very best theoretical treatment of the problem 
of the relation of price to the quantity of commodity, 
and to suggest, from the results of the preceding pages 



82 Economic Cycles: Their Law and Cause 

of this chapter, how imaginary, theoretical difficulties 
are dispelled by solving real problems. 

Of course it is theoretically possible when there is a 
deficiency in the production of corn, that oats, hay, and 
potatoes may be substituted in part for corn, but in- 
stead of conjuring up these and other possibilities that 
are never tested, would it not be wise to ascertain first 
just how closely is the variation in the price of corn 
related to the variation in its own supply? When the 
statistical investigation is made and it is found that 
the correlation coefficient is r = — .789, and that when 
a skew relation is assumed instead of the usual linear 
relation, the connection between the variables is still 
closer, one sees very clearly, if our illustration is a 
typical case, that for most of the problems of actual 
Ufe, it is unnecessary to face the complex possible in- 
terrelation of phenomena contemplated in the theoret- 
ical treatment. For the sake of economy of time and 
of talent, theoretical and statistical work should go 
hand in hand. Even the complex theoretical problem 
that has just been sketched may be tested as to its 
hypotheses and conclusion by the statistical method 
of multiple correlation. 

Elasticity of Demand 

The coefficient of the elasticity of demand for a 
commodity has been described as the ratio of the rela- 
tive change in the quantity of the commodity demanded 
to the relative change in the price, when the relative 
changes are infinitesimal. Starting with this descrip- 



The Law of Demand 83 

tion, we are able, by means of the laws of demand for 

the several commodities, to measure their respective 

degrees of elasticity of demand. It will be recalled that, 

in the form in which the laws of demand have been 

presented in preceding pages, the variable x has been 

taken to represent the relative change in the quantity 

of the commodity, and the variable y, the corresponding 

relative change in the price. The coefficient of the 

dx 
elasticity of demand, therefore, is equal to -j- when x is 

zero. All that is needed to obtain the measure of the 
degree of elasticity of demand is to differentiate y with 
respect to x in the equation to the law of demand, 
place X = zero, and then take the reciprocal of the result. 
The method may be illustrated in case of the four 
representative commodities, corn, hay, oats, and pota- 
toes. The law of demand for corn — see Figure 17 — is 

y = .94- 1.0899a: + .02391a:2- .000234a:' 
Therefore, ^ = - 1-0899 + 2(.02391)a:-3(.000234)a:2 

When a: = 0,1^ = -1.0899, ^ =-rnL^ = --92 
ax ay 1.0899 

and consequently the coefficient of the elasticity of 

demand for corn is —.92. Since the law of demand for 

hay is 

y = 4. 17-.946a: -.0077x2 + .000385a;' 

-^ = —.946 when x = zero, 
dx 

and the coefficient of elasticity of demand is —1.06. 
For similar reasons the degrees of elasticity of demand 



84 Economic Cycles: Their Law and Cause 

for oats and for potatoes are respectively, — .84 and 
-.66. 

In obtaining these numerical values for the coefficient 
of elasticity, the laws of demand for the respective 
crops have been assumed to be parabolas of the third 
order. If the linear laws of demand had been taken for 
the purpose, the coefficients of elasticity would have 
been different. For example, the law of demand 
for corn — see Figure 16 — is y= — .8896.tH-7.79 which 

dv dx 

would give ^=—.8896, or ^=—1.12, whereas the 

coefficient was — .92 in case of the more complex curve. 
This discrepancy between the results when different 
types of curves are used for the demand curve shows the 
need of care in drawing conclusions that are based upon 
numerical values of the coefficient of elasticity. The 
discrepancy does not invalidate the method. When 
different measures of degrees of elasticity are afforded 
by different types of curves, there is a perfectly satis- 
factory criterion which makes it possible to decide 
between different coefficients of elasticity: The coeffi- 
cient is to be preferred which is deduced from the de- 
mand curve that fits the data with the highest degree of 
probability. The demand curve that fits best the data 
affords the best measure of the degree of elasticity of 
demand. 

The conclusions of this chapter may be briefly sum- 
marized. In the closing quarter of the last century 
great hopes were entertained by economists with 
regard to the capacity of economics to be made an 



The Law of Demand 85 

''exact science." According to the view of the foremost 
theorists, the development of the doctrines of utiHty 
and value had laid the foundation of scientific economics 
in exact concepts, and it would soon be possible to 
erect upon the new foundation a firm structure of 
interrelated parts which, in definiteness and cogency, 
would be suggestive of the severe beauty of the 
mathematico-physical sciences. But this expectation 
has not been realized. On the contrary, faith in the 
possibility of an adequate "exact" treatment of the 
science has ■progressively diminished, and interest in 
economic theory in general has decidedly lost ground. 
There must have been something fundamentally wrong 
with the traditional handlmg of the subject, for cer- 
tainly it must be admitted that the parts of a science 
most worthy of study are precisely those parts which are 
concerned with the general and the universal. WTiy, 
then, should there have been the gradual dissipation of 
interest in theoretical economics? 

The explanation is found in the prejudiced point of 
view from which economists regarded the possibilities of 
the science and in the radically wrong method which 
they pursued. It was assumed gratuitously that 
economics was to be modeled on the simpler mathe- 
matical, physical sciences, and this assumption created 
a prejudice at the outset both in selecting the data to be 
investigated and in conceiving of the types of laws that 
were to be the object of research. Economics was 
to be a ''calculus of pleasure and pain," a "mechanics of 
utility," a "social mechanics," a '^physique sodale." 



86 Economic Cycles: Their Law and Cause 

The biased point of view implied in these descriptions 
led to an undue stressing of those aspects of the science 
which seemed to bear out the pretentious metaphors. 
One would naturally suppose from this manner of 
conceiving the science that the economic theorists 
would at once have entered upon their task with the 
methods that had proved themselves useful in the 
physical sciences. But this they did not do. They 
seemed to identify the method of physical sciences with 
experimentation, and since, as they held, scientific 
experimentation is impossible in social life, a special 
method had to be devised. The invention was a dis- 
guised form of the classical cceteris paribus, the method 
of the static state. 

The point of view that has been exemplified in this 
chapter is that the facts in their full concreteness must 
never be lost from sight ; that the laws which are sought 
are of necessity, at first, proximate laws, laws that 
obtain in full empirical reality, and are means of arriv- 
ing at laws of larger generality; that the method to be 
followed is the method which makes progress from the 
data to generalization by a progressive synthesis — 
the method of statistics.^ 

1 With regard to the methodology of the social sciences, the 
writings of Cournot are always helpful. The following quotation 
is taken from a treatise published thirteen years after his epoch 
making Recherches sur les ■princi'pes mathematiques de la theorie des 
richesses. 

Si nous restons dans I'ordre des causes secondaires et des faits 
observables, le seul auquel la science puisse atteindre, la theorie 
math^matique du hasard . . . nous apparait comme I'application 
la plus vaste de la science des nombres, et celle qui justifie le mieux 



The Law of Demand 87 

Starting with this point of view and pursuing the 
method that has just been described, we have attacked 
the old problem of the form of the law of demand. We 
have obtained the concrete laws of demand for repre- 
sentative commodities, have affixed the degree of preci- 
sion with which the laws may be used as formulae for 
predicting prices, and have measured the elasticity of 
demand for the respective commodities. 

In all likelihood it will be said that what we have 
achieved is not exactly what the partisans of the method 
of ccBteris paribus proposed. To this criticism we reply 
that their immediate problem of the relation of price and 
quantity of commodity, cceteris paribus, was vaguely 
conceived and actually abandoned by those who sought 
to give it definiteness, as being incapable of concrete 

I'adage: Mundum regiint numeri. En effet, quoiqu'en aient pens6 
certains philosophes, rien ne nous autorise a croire qu'on puisse 
rendre raison de tous les ph^nomenes avec les notions d'^tendue, de 
temps, de mouvement, en un mot, avec les seules notions des grand- 
eurs continues sur lesquelles portent les mesures et les calculs du 
gfeometre. Les actes des etres vivants, intelligents et moraux ne 
s'expliquent nullement, dans I'etat de nos connaissances, et il y a 
de bonnes raisons de croire qu'ils ne s'expliqueront jamais par la 
mdcanique et la g^om^trie. lis ne tombent done point, par le cotd 
g^om^trique ou m^canique dans le domaine des nombres, mais ils 
s'y retrouvent places, en tant que les notions de combinaison et de 
chance, de cause et de hasard, sont superieures, dans Fordrc des 
abstractions, k la g^om^trie et a la mecanique, et s'appliquent aux 
ph^nomenes de la nature vivante comme k ceux que produisent les 
forces qui sollicitent la mati^re inorganique; aux actes r^fl^chis des 
^tres libres, comme aux determinations fatales de I'app^tit et de 
r instinct. 

Essai sur les fondements de nos cotmaissances et stir les caractires 
de la critique philosophique, vol. 1, pp. 64-65. 



88 Economic Cyces: T heir Law and Cause 

solution; that when the problem is clearly stated, it 
admits of solution by means of a method which we have 
indicated, the method of multiple correlation; and that 
what we have achieved is the solution of their ultimate 
problem of the relation of price and quantity of com- 
modity in a dynamic society. 



APPENDIX 



TABLE I. — The Production and the Price of Corn in the 
United States 







AVEKAOE 








Production op 


Farm Price 


Percentage 


Percentaoe 


Year 


Corn in Thou- 


Per Bushel 


Change in 


Change in 




sands OF Bushels 


December 1, 
IN Cents 


Production 


Price 


1866 


867,946 


47.4 






1867 


768,320 


57.0 


—11.48 


+ 19.41 


1868 


906,527 


46.8 


-f-17.99 


—17.89 


1869 


874,320 


59.8 


— 3.55 


+27.78 


1870 


1,094,255 


49.4 


+25.15 


—17.39 


1871 


991,898 


43.4 


— 9.35 


—12.15 


1872 


1,092,719 


35.3 


+ 10.17 


—18.66 


1873 


932,274 


44.2 


—14.68 


+25.21 


1874 


850,148 


58.4 


— 8.81 


+32.13 


1875 


1,321,069 


36.7 


+55.39 


—37 . 16 


1876 


1,283,828 


34.0 


— 2.82 


— 7.36 


1877 


1,342,558 


34.8 


+ 4.57 


+ 2.35 


1878 


1,388,219 


31.7 


+ 3.40 


— 8.91 


1879 


1,547,902 


37.5 


+ 11.50 


+ 18.30 


1880 


1,717,435 


39.6 


+ 10.95 


+ 5.60 


1881 


1,194,916 


63.6 


—30.42 


+60.61 


1882 


1,617,025 


48.5 


+35.33 


—23.74 


1883 


1,551,067 


42.4 


— 4.08 


—12.58 


1884 


1,795,528 


35.7 


+ 15.76 


—15.80 


1885 


1,936,176 


32.8 


+ 7.83 


— 8.12 


1886 


1,665,441 


36.6 


—13.98 


+ 11.59 


1887 


1,456,161 


44.4 


—12.57 


+21.31 


1888 


1,987,790 


34.1 


+36.51 


—23.20 


1889 


2,112,892 


28.3 


+ 6.29 


—17.01 


1890 


1,489,970 


50.6 


—29.48 


+78.80 


1891 


2,060,154 


40.6 


+38.27 


—19.76 


1892 


1,628,464 


39.4 


—20.95 


— 2.96 


1893 


1,619,496 


36.5 


— .55 


— 7.36 


1894 


1,212,770 


45.7 


—25.11 


+25.21 


1895 


2,151,139 


25.3 


+77.37 


—44.64 


1896 


2,283,875 


21.5 


+ 6.17 


—15.02 


1897 


1,902,968 


26.3 


—16.68 


+22.33 


1898 


1,924,185 


28.7 


+ 1.11 


+ 9.13 


1899 


2,078,144 


30.3 


+ 8.00 


+ 5.57 


1900 


2,105,103 


35.7 


+ 1.30 


+ 17.82 


1901 


1,522,520 


60.5 


—27.67 


+69.47 


1902 


2,523,648 


40.3 


+65.75 


—33.39 


1903 


2,244,177 


42.5 


—11.07 


+ 5.46 


1904 


2,467,481 


44.1 


+ 9.95 


+ 3.76 


1905 


2,707,994 


41.2 


+ 9.75 


— 6.58 


1906 


2,927,416 


39.9 


+ 8.10 


— 3.16 


1907 


1 2,592,320 


51.6 


—11.45 


+29.32 


1908 


: 2,668,651 


60.6 


+ 2.94 


+ 17.44 


1909 


2,772,376 


59.6 


+ 3.89 


— 1.65 


1910 


^ 2,886,260 


48.0 


+ 4.11 


—19.46 


1911 


1 2,531,488 


61.8 


—12.29 


+28.75 



89 



90 



Economic Cycles: Their Law and Cause 



TABLE II. — The Production and the Price of Hay in the 
United States 



Year 


Production of 
Hay in Thou- 
sands OF Tons 
(Ton = 2000 lbs.) 


Average Farm 

Price Per Ton 

December 1, 

in Dollars 


Percentage 
Change in 
Productio.n 


Percentage 

Change in 

Price 


1866 


21,779 


10.14 






1867 


26,277 


10.21 


+20.65 


+ .69 


1868 


26,142 


10.08 


— 2.42 


— 1.27 


1869 


26,420 


10.18 


+ 1.06 


+ .99 


1870 


24,525 


12.47 


— 7.17 


+22.50 


1871 


22,239 


14.30 


— 9.32 


+ 14.68 


1872 


23,813 


12.94 


+ 7.08 


— 9.51 


1873 


25,085 


12.53 


+ 5.34 


— 3.17 


1874 


25,134 


11.94 


+ .20 


— 4.71 


1875 


27,874 


10.78 


+ 10.90 


— 9.72 


1876 


30,867 


8.97 


+ 10.74 


—16.79 


1877 


31,629 


8.37 


+ 2.47 


— 6.69 


1878 


39,608 


7.20 


+25.23 


—13.98 


1879 


35,493 


9.32 


—10.39 


+29.44 


1880 


31,925 


11.65 


—10.05 


+25.00 


1881 


35,135 


11.82 


+ 10.05 


+ 1.46 


1882 


38,138 


9.73 


+ 8.55 


—17.68 


1883 


46,864 


8.19 


+22.88 


—15.83 


1884 


48,470 


8.17 


+ 3.43 


— .24 


1885 


44,732 


8.71 


— 7.71 


+ 6.61 


1886 


41,796 


8.46 


— 6.56 


— 2.87 


1887 


41,454 


9.97 


— .82 


+ 17.86 


1888 


46,643 


8.76 


+ 12.52 


—12.14 


1889 


66,831 


7.04 


+43.27 


—19.63 


1890 


60,198 


7.87 


— 9.93 


+ 11.79 


1891 


60,818 


8.12 


+ 1.03 


+ 3.18 


1892 


59,824 


8.20 


— 1.63 


+ .99 


1893 


65,766 


8.68 


+ 9.93 


+ 5.85 


1894 


54,874 


8,54 


—16.56 


— 1.61 


1895 


47,079 


8.35 


—14.21 


— 2.22 


1896 


59,282 


6.55 


+25.92 


—21.56 


1897 


60,665 


6.62 


+ 2.33 


+ 1.07 


1898 


66,377 


6.00 


+ 9.42 


— 9.37 


1899 


56,656 


7.27 


—14.65 


+21.17 


1900 


50,111 


8.89 


—11.55 


+22.28 


1901 


50,591 


10.01 


+ .96 


+ 12.60 


1902 


59,858 


9.06 


+ 18.32 


— 9.50 


1903 


61,306 


9.07 


+ 2.42 


+ .11 


1904 


60,696 


8.72 


— 1.00 


— 3.86 


1905 


60,532 


8.52 


— .27 


— 2.29 


1906 


57,146 


10.37 


— 5.59 


+21.71 


1907 


63,677 


11.68 


+ 11.43 


+ 12.63 


1908 


70,798 


8.98 


+ 11.18 


—23.12 


1909 


64,938 


10.62 


— 8.28 


+ 18.26 


1910 


60,978 


12.26 


— 6.10 


+ 15.44 


1911 


47,444 


14.64 


—22.19 


+ 19.41 



The Law of Demand 



91 



TABLE III. — The Production and the Price of Oats in the 
United States 







Average 








Production op 


Farm Price 


Percentage 


Percentage 


Ye.vk 


Oats in Thou- 


Per Bushel 


Change i.n 


Change in 




sands OF Bushels 


December 1, 
in Cents 


Production 


Price 


1866 


268,141 


35.1 






1867 


278,698 


44.5 


+ 3.94 


+26.78 


1868 


254,961 


41.7 


— 8.52 


— 6.29 


1869 


288,334 


38.0 


+ 13.09 


— 8.87 


1870 


247,277 


39.0 


—14.24 


+ 2.63 


1871 


255,743 


36.2 


+ 3.42 


— 9.66 


1872 


271,747 


29.9 


+ 6.26 


—17.40 


1873 


270,340 


34.6 


— .52 


+ 15.72 


1874 


240,369 


47.1 


—11.09 


+36.13 


1875 


354,318 


32.0 


+47.41 


—32.06 


1876 


320,884 


32.4 


— 9.44 


+ 1.25 


1877 


406,394 


28.4 


+26.65 


—12.35 


1878 


413,579 


24.6 


+ 1.77 


—13.38 


1879 


363,761 


33.1 


—12.05 


+34.55 


1880 


417,885 


36.0 


+ 14.88 


+ 8.76 


1881 


416,481 


46.4 


— .34 


+28.89 


1882 


488,251 


37.5 


+ 12.43 


—19.18 


1883 


571,302 


32.7 


+ 17.01 


—12.80 


1884 


583,628 


27.7 


+ 2.16 


—15.29 


1885 


629,409 


28.5 


+ 7.84 


+ 2.89 


1886 


624,134 


29.8 


— .84 


+ 4.56 


1887 


659,618 


30.4 


+ 5.68 


+ 2.01 


1888 


701,735 


27.8 


+ 6.39 


— 8.55 


1889 


751,515 


22.9 


+ 7.09 


—17.63 


1830 


523,621 


42.4 


—30.32 


+85.15 


1891 


738,394 


31.5 


+41.02 


—25.71 


1892 


661,035 


31.7 


—10.48 


+ .63 


1893 


638,855 


29.4 


— 3.36 


— 7.26 


1894 


662,037 


32.4 


+ 3.63 


+ 10.20 


1895 


824,444 


19.9 


+24.53 


—38.58 


1896 


707,346 


18.7 


—14.20 


— 6.03 


1897 


698,768 


21.2 


— 1.21 


+ 13.37 


1898 


730,907 


25.5 


+ 4.60 


+20.28 


1899 


796,178 


24.9 


+ 8.93 


— 2.35 


1900 


809,126 


25.8 


+ 1.63 


+ 3.61 


1901 


736,809 


39.9 


— 8.94 


+54.65 


1902 


987,843 


30.7 


+34.07 


—23.06 


1903 


784,094 


34.1 


—20.52 


+ 11.07 


1904 


894,596 


31.3 


+ 14.09 


— 8.21 


1905 


953,216 


29.1 


+ 6.55 


— 7.03 


190o 


964,905 


31.7 


+ 1.23 


+ 8.93 


1907 


754,443 


44.3 


—21.81 


+39.75 


1908 


807,156 


47.2 


+ 6.99 


+ 6.55 


1909 


1,007,353 


40.5 


+24.80 


—14.19 


1910 


1,186,341 


34.4 


+ 17.77 


—15.06 


1911 


922,298 


45.0 

1 


—22.26 


+30.81 



92 



Economic Cycles: Their Law and Cause 



TABLE IV. — The Production and the Price of Potatoes in 
THE United States 





Production op 

Potatoes i.v 

Thousands of 

Bushels 


Average 
Farm Price 


Percentage 


Percentage 


Year 


Per Bushel 


Change in 


Change in 




December 1, 


Production 


Price 






IN Cents 






1866 


107,201 


47.3 






1867 


97,783 


65.9 


— 8.79 


+39.32 


1868 


106,090 


59.3 


+ 8.50 


—10.02 


1869 


133,886 


42.9 


+26.20 


—27.66 


1870 


114,775 


65.0 


—14.27 


+51.52 


1871 


120,462 


53.9 


+ 4.95 


—17.08 


1872 


113,516 


53.5 


— 5.77 


— .74 


1873 


106,089 


65.2 


— 6.54 


+21.87 


1874 


105,981 


61.5 


— .10 


— 5.67 


1875 


166,877 


34.4 


+57.46 


—44.07 


1876 


124,827 


61.9 


—25.20 


+79.94 


1877 


170,092 


43.7 


+36.26 


—29.40 


1878 


124,127 


58.7 


—27.02 


+34.32 


1879 


181,626 


43.6 


+46.32 


—25.72 


1880 


167,660 


48.3 


— 7.69 


+ 10.78 


1881 


109,145 


91.0 


—34.90 


+88.41 


1882 


170,973 


55.7 


+56.65 


—38.79 


1883 


208,164 


42.2 


+21.75 


—24.24 


1884 


190,642 


39.6 


— 8.42 


— 6.16 


1885 


175,029 


44.7 


— 8.19 


+ 12.88 


1886 


168,051 


46.7 


— 3.99 


+ 4.47 


1887 


134,103 


68.2 


—20.20 


+46.04 


1888 


202,365 


40.2 


+50.90 


^1.06 


1889 


204,881 


35.4 


+ 1.24 


—11.94 


1890 


148,290 


75.8 


—27.62 


+ 114.12 


1891 


254,424 


35.8 


+71.57 


—52.77 


1892 


156,655 


66.1 


—38.43 


+84.64 


1893 


183,034 


59.4 


+ 16.84 


—10.14 


1894 


170,787 


53.6 


— 6.69 


— 9.76 


1895 


297,237 


26.6 


+74.04 


—50.37 


1896 


252,235 


28.6 


—15.14 


+ 7.52 


1897 


164,016 


54.7 


—34.97 


+91.26 


1898 


192,306 


41.4 


+ 17.25 


—24.31 


1899 


228,783 


39.0 


+ 18.97 


— 5.80 


1900 


210,927 


43.1 


— 7.80 


+ 10.51 


1901 


187,598 


76.7 


—11.06 


+77.96 


1902 


284,633 


47.1 


+51.72 


—38.59 


1903 


247,128 


61.4 


—13.18 


+30.36 


1904 


332,830 


45.3 


+34.68 


—26.22 


1905 


260,741 


61.7 


—21.66 


+36.20 


1906 


308,038 


51.1 


+ 18.14 


—17.18 


1907 


298,262 


61.8 


— 3.17 


+20.94 


1908 


278,985 


70.6 


— 6.46 


+ 14.24 


1909 


376,537 


54.9 


+34.97 


—22.24 


1910 


349,032 


55.7 


— 7.30 


+ 1.46 


1911 


292,737 


79.9 


—16.13 


+43.45 



CHAPTER V 

THE MECHANISM OF CYCLES 

"Agriculture is the Foundation of Manufacture and Commerce." 
— Motto of the United States Department of Agriculture. 

Thus far in our investigation of the cause and law of 
economic cycles, we have shown that the annual rainfall 
in the principal grain-producing area of the United 
States passes through definite, well-defined cycles; and 
that the yield of typical, leading crops is so closely 
related to the rainfall of theu' respective critical seasons 
that the cyclical movement of the rainfall of the critical 
seasons is approximately reproduced in the yield per 
acre of the corresponding crops. These cycles of crops 
constitute the natural, material current which drags 
upon its surface the lagging, rhythmically changing 
values and prices with which the economist is more 
immediately concerned. In order to understand the 
connection between the flow of the undercurrent of 
agricultural yield and the surface changes of values and 
prices, we have taken the necessary first step of con- 
necting the prices of agricultural commodities with 
their supply. But the supply varies with the acreage as 
well as with the yield, and consequently to carry further 
our investigation we must know how closely the prices 
of crops are related to their yield. 

93 



94 Economic Cycles: Their Law and Cause 

The Prices of Agricultural Commodities Correlated with 
the Yield of the Several Crops 

The method employed in the preceding chapter to 
derive the law of demand of the several crops contained 
two stages : As a first stage, the correlation between the 
relative change in the total supply and the correspond- 
ing relative change in price was assumed to be linear, 
and upon the hypothesis of linearity of regression, the 
demand curve was computed and the degree of accuracy 
with which prices might be predicted from such linear 
demand curves we showed how to measure. The second 
stage in the theory of demand curves was to assume a 
skew relation between relative changes in price and 
supply, and we found that the degree of accuracy with 
which prices might be predicted from the skew demand 
curves was greater than when the law of demand was 
assumed to be linear. We shall follow these two stages 
in treating the relation between the yield per acre and 
the price of the crops. 

If the correlation between the relative change in 
yield per acre and the relative change in price is as- 
sumed to be linear, we obtain for the coefficients of 
correlation in case of the four typical crops, the values 
placed in the first row of the accompanying Table, 
which, for purpose of comparison, also presents the 
corresponding coefficients in case of the linear demand 
curves. 



The Mechanism of Cycles 



95 



A Comparison of the Coefficients of Correlation in 
Case of Linear Yield-Price Curves and of Linear 
Demand Curves 





Corn 


Hay 


Oats 


Potatoes 


Relative change in 










yield per acre and 
relative change in 


— .815 


— .656 


— .718 


— .873 


price 










Relative change in 










total supply and 
relative change in 


— .789 


— .715 


— .722 


— .856 


price 








J 



The data used in the above computation were, in 
case of the yield-price curve, the average yield per acre 
of the respective crops in the whole of the United 
States and the corresponding average prices for the 
United States, on tHe first of December of the years in 
which the crops were produced. The data for the 
demand curves, it will be recalled from the preceding 
chapter, were the total supply of the respective crops 
in the United States and the corresponding prices on 
December 1. The period covered in both cases was 
from 1866 to 1911, inclusively. The data were ob- 
tained from recent Yearbooks of the United States 
Department of Agriculture. 

It appears, from the coefficients of correlation given 
in the above Table, that it is possible to predict the 
prices of the crops from the yield per acre with the same 



96 Economic Cycles: Their Law and Cause 

precision with which prices may be predicted from the 
demand curves. Or, to put the idea in another form, 
the productivity of the soil is as closely related to the 
prices of crops as the supply of the commodity is related 
to the same prices. In the chapter on the "Law of 
Demand," we found that, when the relative change in 
the supply is given, the mean shift in the corresponding 
change of price may be obtained from the regression 
equation, and that, furthermore, the root-mean-square 
deviation of the observations may be computed by 
the formula S = ^y^l—r''. This same formula may 
be used for a similar purpose in case of the yield-price 
curves. 

We come now to the second stage in the derivation of 
the relation between price and the yield per acre of 
crops. We assume that the relation between the yield 
per acre and the price of a crop is skew, and that the 
relation between the two may be expressed by an 
equation of the iormy =a-{-bx-\-cx'^+dx^. 

In Figure 21, the skew yield-price curves of our four 
representative commodities are drawn to a percentage 
scale. The equations to the curves, which were com- 
puted by the Method of Least Squares, are given upon 
the Figure. The root-mean-square deviation of the 
observations from their respective yield-price curves 
are given in the following Table which, for purposes 
of comparison, reproduces the coefficients that were 
found, in the preceding chapter, to measure the devia- 
tion of the observations about the skew laws of de- 
mand. 



The Mechanism of Cycles 



97 



the yie/d per acre of hay. 




Percentage chanie In the yield per acre ofosts Percentage change in the yield per acre of potatoes 



Figure 21. The relation between the price and the yield per acre of the 

several crops. 
When the origin is at (0, 0), the equations are 

For corn, y = .17 — 1.2989x + .01892^2 — .000137x'. 
For hay, y = 1.17 — 1.0215x + .01549x2 + .00009x'. 
For oats, y = — 1.49 — 1.1346x + .02324x2 — .000238x3. 
For potatoes, ?/ = .49 — 1.4863x + .01993x2 — .000141x'. 



98 Economic Cycles: Their Law and Cause 



A Comparison of the Root-Mean-Square Deviation in 
Case of Skew Yield-Price Curves and of Skew De- 
mand Curves 





Corn 


Hay 


Oats 


Potatoes 


Yield-Price 
Curves 


5.48 


5.72 


7.05 


9.39 


Demand 
Curves 


7.36 


4.65 


10.17 


9.94 



From the results given in the last two Tables, it is clear 
that the prices of the representative crops are as closely 
related to the yield per acre as to the total supply of the 
crops. This conclusion is of importance in the task of 
connecting the cycles in the productivity of the soil with 
the cycles in values and prices. 

In obtaining the preceding close relations between the 
changes in prices and changes in yield, the figures for the 
whole of the United States were employed. The object 
of broadening the field of observation from the detailed 
investigation of the Middle West to the whole of the 
United States was two-fold: First, it seemed likely, a 
-priori, that a more intimate relation between prices and 
yield would be obtained if the large market of the whole 
country were substituted for the local market of Ilhnois; 
secondly, because the object of this chapter is to bring 
the physical cycles of crops into relation with the 
industrial and commercial changes of the whole country, 
and to this end it seemed desirable that the crops of the 



The Mechanism of Cycles 99 

whole country should be considered. We need, how- 
ever, to assure ourselves that, in taking this more 
comprehensive view of the yield of crops, we have not 
lost the characteristic cyclical movement of the yield 
which we discovered in the more limited study. We 
desire to know how closely the yield per acre of the 
whole country is correlated with the yield per acre of 
our representative state of Illinois. 

The correlations of the annual differences in the yield 
per acre in Illinois and the annual differences in the 
yield per acre in the United States were, in case of our 
four typical crops, for corn, r = .855; for hay, r = .745; 
for oats, r = .800; for potatoes, r = .843. The period 
covered in all cases was from 18GG to 1912 inclusively. 
The data were obtained from Bulletins, 56, 58, 62, 63 
of the Bureau of Statistics of the United States Depart- 
ment of Agriculture and from the recent Yearbooks of 
the same Department. A reference to the Table given 
a moment ago will show that the yield per acre of crops 
in Illinois is at least as closely related to the yield per 
acre of the same crops in the United States, as the prices 
of the several crops are related either to the supply 
of the crops or to the yield per acre of the crops. More- 
over, the very high values of the coefficients leave but 
little room for doubt that the cyclical movement of the 
yield per acre in the Middle West is representative of 
the movement of the crop yield in the whole of the 
United States. 



100 Economic Cycles: Their Law and Cause 

Rising and Falling Prices as Related to Yield-Price 

Curves 

Thus far it is clear that the prediction of agricul- 
tural prices is dependent upon a knowledge (1) of the 
law of the variations of price with the yield per acre, 
and (2) of the law of the annual change in the yield per 
acre of the several crops. If the relation between prices 
and yield per acre were constant, the theory of agricul- 
tural cycles would be completely elucidated; for, once 
having discovered the law of the relation of price to 
yield per acre, nothing more would be necessary then 
to connect the yield with the meteorological conditions 
of its critical season, and the resulting prices for a long 
term of years could be predicted with great probability. 
But the relation between the price of the crops and the 
yield per acre varies with the level of general prices, and 
it is of the first importance to know the manner of varia- 
tion. 

If the course of prices in the United States for the 
period 1866 to 1911 is examined, it will be seen that, 
in general terms, we may with justness characterize the 
period 1866 to 1890 as a period of falhng prices, and the 
period 1890 to 1911 as a period of rising prices. If 
therefore, in case of each of our representative com- 
modities, we construct two yield-price curves, one 
for the period of falling prices and one for the pe- 
riod of rising prices, we shall, by comparing the two 
curves for the two periods, discover how the demand 
curves, or yield-price curves, vary in periods in which 



The Mechanism of Cycles 101 

the movement of general prices is in opposite direc- 
tions. 

In Figure 22, the eight curves are drawn. Compar- 
ing the curves in the two periods for each of the four 
representative crops we infer that 

(1) the demand schedule or yield-price curve is high 

when the general level of prices is high; and 
the demand schedule is low when the general 
level of prices is low; 

(2) the general run of the curves remains nearly the 

same. That is to say, the principal difference 
between the period of falling prices and period 
of rising prices is that the yield-price schedules 
move down or up. 

These are general statements in which quite obvious 
deviations are ignored and which, consequently, do 
not pretend to quantitative accuracy. The construc- 
tion of the curves is dependent upon too few observa- 
tions to admit of attaching significance to the apparent 
exceptions to the rule. 

Since the prices of the representative crops are, as we 
know, dependent upon the yield per acre and the law 
of the relation between prices and the yield per acre, 
and since, as we have proved, the yield-price curves 
move with the general level of prices, our desideratum 
is to discover what determines the change in the level 
of general prices. 



102 Economic Cycles: Their Law and Cause 









C^ 




^ 
<: 



0. 



^-s 



'^-'. 



Pfreenfofe change in the yield pfr acre o/'corn fhrtrenfg^e chande in the yield per acre of hay. 

,1 




Ks^ 



^ 



Percenhide chande in fhe yield per acre of oafs. ^erreniade change in the yield per acre of potatoes. 

Figure 22. The relation between the price and the yield per acre of the 

several crops. 
When the origin is at (0,0), the equations are 



For corn 



For hay 



For oats 



For potatoes 



yrs. 1866-1889 
yrs. 1890-1911 
yrs. 1866-1889 
yrs. 1890-1911 

[ yrs. 1866-1889 
yrs. 1890-1911 
yrs. 1866-1889 

[yrs. 1890-1911 



_,?/=— 2.00— 

, ?/ = 3.06 

_-_,2/ = -5.72- 
—,y= 5.41— 
--,2/ = -2.78- 
— ,2/= .99- 
_..,2/ = -3.92- 
— ,y = - .91- 



1.0299x-f- 
1.4894x4- 
1.6435X + 
.7306x— 
1.6039X— 
1.0240X + 
1.4424x4- 
1.6068x4- 



.01926x^ 

.01737x2 

.07798x2— 

.00591x2+ 

.00546x2-h 

.02394x2— 

.01684x2— 

.03831x2— 



.0003 12x\ 
.000049x3. 
000574x». 
.000075x3. 
.000778x3. 
.000383x3. 
.000020x3. 
.000397x». 



The Mechanism of Cycles 103 

The Volume of Crops and the Activity of Industry 

We shall approach the problem of the cause of the 
changing level of prices by considering two preliminary 
questions which will enter into the subsequent argu- 
ment: (1) Is there any relation between the changing 
volume of the crops and the changing volume of those 
producers' goods whose fluctuations are generally re- 
garded as indices of the activity of trade? (2) Is the 
law of demand for crops the type of law that is repro- 
duced in the demand for all conmiodities, or is it not 
rather the case that the law of demand for pure pro- 
ducers' goods is of a different type from the law of 
demand for those commodities of which our four crops 
are samples? 

The first of these two questions we shall consider in a 
form modified to bring its significance to bear upon the 
results that have already been established. The volume 
of crops varies with the extent of the acreage and with 
the average yield per acre. The question of interest 
to us at this point is whether the volume of producers' 
goods fluctuates with the yield per acre of the crops. 
We shall investigate this question, and, as a means of 
carrying forward our inquiry, we first construct an 
index number of the yield per acre of crops. The nine 
crops of the United States whose yield per acre through- 
out a long period is recorded in the Yearbooks of the 
Department of Agriculture are : corn, wheat, oats, bar- 
ley, rye, buckwheat, potatoes, hay, cotton.^ If, in case 
» The figures for the yield per acre of cotton, 1870-1910, were ob- 



104 Economic Cycles: Their Law and Cause 

of each of these crops, the mean yield per acre for the 
years 1890-1899 is taken as a base, and the yield per 
acre for each of the years 1870-1911 is expressed as a 
ratio of the base, comparable indices for the crops dur- 
ing the period of forty-two years will be obtained. In 
order to combine the nine series of figures into a series 
that shall be representative of the whole of agriculture, 
the several series must be properly weighted. The 
method of weighting that was adopted in this particular 
case was to assign to each crop an importance propor- 
tionate to its value as compared with the total value of 
the nine crops in 1911. The several weights were: for 
corn, 36; wheat, 12; oats, 9; barley, 3; rye, .7; buck- 
wheat, .3; potatoes, 6; hay, 16; cotton, 17. The index 
numbers are given in Table I of the Appendix to this 
chapter. 

Before comparing the index number for the yield 
per acre of the crops with the volume of producers' 
goods, we must make sure that we are keeping close 
to the results obtained from a detailed investigation 
of our four representative crops. If an index number of 
the four representative crops is constructed upon the 
same principle as the index for the nine crops, how 
closely would the indices be correlated? In computing 
the index of the yield per acre of the four representa- 
tive crops, the weights assigned were: for corn, 50; 
hay, 28; oats, 15; potatoes, 7. The index is given in 

tained from Circular 32, Bureau of Statistics, U. S. Department of 
Agriculture. The yield for 1911 was obtained from the Yearbook 
of the Department of Agriculture, 1911. 



The Mechanism of Cycles 105 

Table I of the Appendix to this chapter. The coeffi- 
cient of correlation between the index for the four 
representative crops and the index for the nine crops, 
is r = .960. 

It is a common observation of writers on economic 
crises that the production of pig-iron is an unusually 
good barometer of trade. The amount of pig-iron 
that is annually produced swells with the activity 
and volume of industry and trade, and it is among the 
first commodities to indicate the general shrinking in 
the ultimate demand which checks the activity of 
trade and causes its temporary decline. Is there any 
relation between the movement of this barometer of 
trade, the production of pig-iron, and the cycles of the 
crops? Can it be that the increase and decrease of the 
"ultimate demand" which lies back of the flow and 
ebb of trade has its source in the cyclical movements 
of the yield per acre of the crops? 

The data for testing whether there is a relation be- 
tween the yield per acre of the crops and the annual 
production of pig-iron are the statistics of the annual 
production of pig-iron and the index numbers of the 
yield per acre of our nine crops. 

The method of testing the relation presents difficul- 
ties, and as it will be used again to measure the relation 
between the cycles of crops and the cycles of general 
prices, we shall have a firmer grasp upon our problem 
if we stop now to gain a clear idea of the terms that 
continually occur in the argument. In any one of the 



106 Economic Cycles: Their Law and Cause 

series of figures that we shall use there are three distinct 
movements which need to be discriminated, and when 
any two of the series are compared, another important 
characteristic of the series requires to be taken into 
account. The three movements that are combined in 
each series are: 

(a) The continuous fall or rise of the figures with the 
flow of time. This movement will be referred 
to as the secular trend of the figures; 
(6) The rhythmical fluctuation of the figures about 
their secular trend. When this movement 
superposed upon the secular trend is the ob- 
ject of investigation, the combined movement 
will be referred to as the general cychcal 
movement of the figures. When the rhyth- 
mical movement unaffected by the complicat- 
ing trend is being considered, it will be referred 
to simply as the cycles of the figures; 
(c) The year to year temporary fluctuation about 
the general cychcal movement. These fluctua- 
tions will be referred to as the deviations of 
the figures. 
When the cycles of any two series are compared, it will 
frequently happen, particularly if the one series is the 
cause of the other, that there is a considerable interval 
between the corresponding parts of the cycles in the 
two series. This interval will be referred to as the lag 
of the second series. 

We shall be interested throughout the rest of this 
chapter primarily in the interrelations of cycles of 



The Mechanism of Cycles 107' 

crops, cycles in the activity of industry, and cycles in 
general prices. But we approach our general problem 
by considering first the temporary fluctuations which 
we have agreed to call deviations, and we inquire 
whether there is a relation between the deviations of 
the yield of the crops and the deviations in the produc- 
tion of pig-iron. The method that was adopted was 
first to obtain the general cyclical movements of the 
two series by averaging, in case of each series, the 
figures for each year with the figures that immediately 
preceded and followed the given year. For example, 
the index number of the yield per acre for the years 
1870, 1871, 1872, 1873 were respectively 108, 105, 110, 
99. The smoothed figure for the yield per acre in 1871 

,, . . , 108 + 105 + 110 323 . 

would therefore be =-— = 107.7. feimi- 

o o 

larly, the smoothed index for 1872 would be 104.7. In ' 
Tables II and III of the Appendix to this chapter are 
presented the original and the smoothed figures for the 
production of pig-iron and for the index number of the 
yield per acre of the nine crops. The statistics of the 
production of pig-iron were obtained from the Statis- 
tical Abstract of the United States for 1912, p. 774. 

After the general cychcal movements of the two series 
were determined, the deviations of the actual figures 
from the smoothed figures for each of the years were 
calculated for both series of figures. These deviations 
are also given in Tables II and III of the Appendix to 
this chapter. The question upon which these differ- 
ences are to throw hght may be put in this form: Is 



108 Economic Cycles: Their Law and Cause 

the deviation of the yield per acre of the crops from its 
general cyclical movement associated with the devia- 
tion, in the following year, of the production of pig- 
iron from the general cyclical movement of pig-iron? 
The answer is found by correlating the differences, 
always remembering that the difference for the yield 
per acre in any given year is to be taken with the dif- 
ference of the production of pig-iron in the following 
year. The coefficient of correlation is r = .254. 

We come now to the association between the cyclical 
movement of the yield per acre of the crops and the 
cyclical movement of the production of pig-iron. Each 
of these movements is superposed upon a rising secular 
trend, and before we can test the degree in which the 
cycles are related the secular trends must be eliminated. 
If, as a first approximation, the secular trend in each 
case is assumed to be linear, then by fitting a straight 
line ^ to the data, it is possible to calculate the fluctua- 
tions of the cycles of crop yield and of production of 
pig-iron about their respective trends, and these fluctua- 
tions may be correlated. In Table IV of the Appendix 
to this chapter, the data for the calculation of the con- 
nection between the cycles are given. In columns 2 
and 5 are tabulated the general cyclical movements of 

1 The equations to the linear secular trends are, respectively, 
2/ = .1844a;-f 98.57, for the yield per acre of crops; and y = 582.7lx+ 
9525, for the production of pig-iron. The origin in the first case is 
at 1871 and in the latter case, at 1890. The first equation was com- 
puted from the data for the years 1871-1906, and the second equa- 
tion, from the data for 1871 to 1910. 



The Mechanism of Cycles 109 

the yield per acre of the crops and of the production of 
pig-iron; in columns 3 and 6, the values of the Hnear 
secular trends are given; and in columns 4 and 7, the 
deviations of the cyclical movement from the secular 
trend are recorded. These last deviations are the ma- 
terial for calculating the connection between the cycles 
of the yield per acre of the crops and the cycles of the 
production of pig-iron. 

If the deviations of the cycles from their respective 
secular trends are correlated, the coefficient of correla- 
tion reaches the value, r = .625, but we must not be 
content to assume that even this relatively high co- 
efficient represents the full degree of the relation be- 
tween the cyclical movement of the crops and the 
cyclical movement of the activity of industry as that 
activity is typified in the production of pig-iron. It is 
quite hkely that the good or bad crops may produce 
their maximum effect at a considerable interval after 
the period in which the crops are actually harvested. 
Time is required for the changing productivity of 
crops to work out its maximum effect, and this causes 
a lag in the adjustment of the cycles of the activity of 
industry to the cycles of the yield of the crops. We 
must therefore measure the amount of the lag. 

If instead of correlating the cycles of the yield of the 
crops and of the production of pig-iron for correspond- 
ing years, we correlate them for lags of various intervals, 
we shall find it possible to determine the lag that will 
give the maximum coefficient of correlation, and this 
particular value of the lag we may then regard as the 



110 Economic Cycles: Their Law and Cause 

interval of time required for the cycles in the crops to 
produce their maximum effect upon the cycles of the 
activity of industry. Wlien the calculation of the co- 
efficients of correlation is made according to this plan, 
it is found that for a lag 

Of zero years, r=.625; 
Of one year, r=.7l9; 
Of two years, r = .718; 
Of three years, r = .697 ; 
Of four years, r = .572. 

It is clear, therefore, that the cycles in the yield per 
acre of the crops are intimately related to the cycles in 
the activity of industry, and that it takes between one 
and two years for good or bad crops to produce the 
maximum effect upon the activity of the pig-iron in- 
dustry. Figure 23 illustrates the general congruence 
of the cycles of the crops and of the cycles in the produc- 
tion of pig-iron when a lag of two years is eliminated. 

As to the general question concerning the relation 
between the harvests and the activity of industry, we 
may conclude from our statistical inquiry that there is 
a positive, intimate connection, and very probably a 
direct causal relation, between the bounty or niggardli- 
ness of nature and the flow or ebb of trade. ^ 

A New Type of Demand Curve 

A moment ago, we saw that two prehminary problems 

had to be treated before we could pass to the direct 

1 In a later section of the chapter the method that has been used 
in treating this problem will be employed for another purpose and 
will then be illustrated in detail by means of graphs. 



The Mechanism of Cycles 



111 



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112 Economic Cycles: Their Law and Cause 

consideration of the cause and law of cycles of general 
prices. The first of these preliminary problems, namely, 
the influence of the bounty of nature upon the volume 
and activity of trade, we have just discussed, and we 
come now to the second preliminary problem, which 
we shall put in the form of a question: Are all demand 
curves in a dynamic society of the same type as the 
demand curves for the representative crops: corn, hay, 
oats, and potatoes? 

This question must be answered as a preliminary to 
the more fundamental inquiry as to the cause of cycles 
of general prices, because if we assume that all demand 
curves are of the same negative type, we are confronted 
with an impossibility at the very beginning of our in- 
vestigation. Upon the assumption that all demand 
curves are of the negative type, it would be impossible 
for general prices to fall while the yield per acre of 
crops is decreasing. In consequence of the decrease 
in the yield per acre, the price of crops would ascend, 
the volume of commodities represented by pig-iron 
would decrease, and upon the hypothesis of the uni- 
versality of the descending type of demand curves, the 
prices of commodities like pig-iron would rise. In a 
period of decUning yield of crops, therefore, there would 
be a rise of prices, and in a period of increasing yield of 
crops there would be a fall of prices. But the facts are 
exactly the contrary. During the long period of falhng 
prices from 1870 to 1890, there was a decrease in the 
yield per acre of the crops, and during the long period 
of rising prices from 1890 to 1911, there was an increas- 



The Mechanism of Cycles 113 

ing yield of crops. It is obviously inadmissible to 
assume that in a dynamic society there is one law of 
demand for all commodities. The dogma of the uni- 
formity of the law of demand is an idol of the static 
state. 

If there are differences in types of demand curves, 
it is quite likely that as one type has been illustrated by 
the crops, another type will be exemplified by pure 
producers' goods. We shall accordingly investigate 
the demand curve of pig-iron, our representative pro- 
ducers' good. 

In Table V of the Appendix to this chapter is con- 
tained the material for the computation of the law of 
demand for pig-iron. The annual percentage changes 
in the production of pig-iron were computed from the 
figures of annual production, which were taken from 
the Statistical Abstract for 1912, p. 774. It was impos- 
sible to obtain directly the mean prices for which the 
annual production was sold, and consequently the per- 
centage change in the mean price could not be com- 
puted directly. The device that was utilized to ap- 
proximate these percentage changes is illustrated in 
Table V of the Appendix. As the data needed for the 
solution of the problem were the annual percentage 
changes in the mean price and not the actual mean 
annual prices themselves, it was regarded as sufficient 
for our purpose to substitute for the unobtainable an- 
nual percentage changes in the mean price, the mean 
annual percentage changes in the prices of representa- 
tive kinds of pig-iron. The annual prices for the lead- 



114 Economic Cycles: Their Law and Cause 

ing four kinds of pig-iron were obtained from the Statis- 
tical Abstract for 1912, p. 572, and the annual percentage 
changes in the prices of the four kinds, together with 
their mean annual percentage changes, are given in 
Table V of the Appendix. The second and last columns 
of Table V were used in computing the law of demand 
for pig-iron in the United States. 

The graph of the law of demand for pig-iron is given 
in Figure 24. The correlation between the percentage 
change in the product and the percentage change in the 
price is r = .537. The equation to the law of demand 
is t/ = . 5211a:— 4.58, the origin being at {o,o). Our re- 
presentative crops and representative producers' good 
exempHfy types of demand curves of contrary charac- 
ter. In the one case, as the product increases or de- 
creases the price falls or rises, while, in the other case, 
the price rises with an increase of the product and falls 
with its decrease. 

The two preliminary difficulties are now cleared 
away. We know that as the yield per acre of the crops 
increases the physical volume of trade for producers' 
goods increases; and we know, furthermore, that the 
law of demand for a representative producers' good is 
such that as the product increases the price increases. 
If now a third fact, which has already been estabUshed, 
be added to these two, an hypothesis conformable to 
the three facts may be made which will give a working 
theory for examining whether the cycles in crops pro- 
duce the cycles in general prices. The third fact to 
which reference is made is that the law of demand for 



The Mechanism of Cycles 



115 




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116 Economic Cycles: Their Law and Cause 

the crops falls during a period of falling general prices, 
and rises during a period of rising general prices. With 
these facts in mind it is not difficult to conceive how 
general prices may fall during a period of diminishing 
yield per acre of the crops and rise during the period 
that the yield is increasing. The falling yield in the 
crops would lead to a diminution of the volume of trade, 
a decline in the demand for producers' goods, a fall in 
the prices of producers' goods, a decrease in employ- 
ment, a fall of the demand curves for crops, with the 
final result of a fall in general prices. Similarly, a 
rising yield in the crops would lead to an increase in 
the volume of trade, an increase in the demand for 
producers' goods, an increase of employment, a rise 
in the demand curves for crops, with the final result of 
a rise in general prices. Provided the interrelation of 
the economic factors are in accordance with this de- 
scription, then it would follow that the cycUcal move- 
ments m the yield of the crops should be reproduced 
in cychcal movements of general prices. If the actual 
facts bear out this deduction, there can be no doubt 
that the cause and law of economic cycles have been 
discovered. 

The Fundamental, Persistent Cause of Economic Cycles 

To put the theory to the test of facts we require an 
index number of general prices throughout the period 
covered by most of the investigation in this Essay — 
the period from 1870 to 1911. There is no one index 
number covering this period for the United States, but 



The Mechanism of Cycles 117 

very fortunately there are two series that overlap in the 
middle of the period, so that it is possible to construct a 
series covering the whole term of years. The two series of 
index numbers in question are the Falkner index for "all 
articles" extending from 1870 to 1890, and the index of 
the Bureau of Labor for ''all commodities" extending 
from 1890 to 1911. Since these two have the year 1890 
in common it is possible, by applying the simple rule of 
proportion, to reduce the Falkner series to the base of 
the series pubHshed by the Bureau of Labor. The two 
original series and the continuous series are given in 
Table VI of the Appendix to this chapter. 

The test of the theory that the cause and law of 
economic cycles are the cyclical movements of the 
yield per acre of the crops will be given in answer to two 
questions: First, are the deviations of the indices of 
general prices from their general cyclical movement 
correlated with the deviations of the indices of the yield 
per acre of the crops from their general cyclical move- 
ment? Secondly, are the cycles of prices and the cycles 
of crops correlated? The answers to these two questions 
are the substance of the following paragraphs. 

In Tables III and VI of the Appendix to this chapter 
are given the indices of the yield per acre of the crops 
and the indices of general prices. The Tables like- 
wise contain the smoothed indices and the deviations of 
the actual indices from the smoothed indices. The 
smoothed series were obtained in the manner that was 
described when the relation between the yield of the 
crops and the production of pig-iron was being treated. 



118 Economic Cycles: Their Law and Cause 

It will be recalled from that description that the 
smoothed index for any given j^ear is the mean of three 
actual indices: the actual index for the given year, the 
actual index for the year preceding the given year, and 
the actual index for the year following the given year. 
The quantities whose correlation is in question are the 
deviations of the actual indices of general prices, and of 
yield per acre, from their respective smoothed series. 
The results of the computation are as follows : 

From 1870-1911, r=.303, 
From 1870-1890, r=.370, 
From 1890-191 1, ;=.250. 

In the first row the correlations were obtained from 
the continuous series in which the Falkner index was 
adjusted to the index of the Bureau of Labor. In the 
second row the correlations were derived from the 
Falkner index unaltered. In the third row the correla- 
tions were computed from the index of the Bureau of 
Labor. We infer that the deviations from their general 
cyclical movement of thejndices of general prices vary 
directly with the deviation from their general cyclical 
movement of the indices of the yield per acre of the 
crops. 

The second of the two questions as to the cause and 
law of the cycles of general prices was stated in this 
form: Are the cycles of prices and the cj^cles of crops 
correlated? The preceding paragraphs have presented 
the results of the inquiry as to the relation between the 
deviations of actual prices and of yield from their 



The Mechanism of Cycles 119 

respective general cyclical movements. The present 
question concerns the relation of the cyclical move- 
ments themselves, after their respective secular trends 
have been eliminated. 

It will be recalled that the general cyclical movements 
were obtained by a process of smoothing the actual 
series of the indices of prices and of yield per acre, the 
process consisting in the formation of a progressive 
mean of the indices for three consecutive years. These 
smoothed series, which are given in Tables III and VI 
of the Appendix to this chapter, form the data of the 
present investigation. 

The method of the investigation is presented in Fig- 
ures 25, 26, 27. In the first of these three Figures, the 
general cyclical movements of prices and of yield per 
acre are described according to the data of Tables III 
and VI. The graphs bring out clearly the rhythmical 
motions of both prices and yield and a comparison 
of the curves suggests that the price curve is a lagging 
reproduction of the yield curve. But before the amount 
of the lag and the degree of correlation between the 
cycles can be computed, the secular trends in the two 
series of values must be eliminated. From Figure 25 it 
is apparent that the price cycles move upon a falling 
secular trend while the yield cycles move upon a rising 
secular trend. If it is assumed as a first approximation 
that these secular trends are both linear, the equation to 
the trend for prices is 7/ = — .3702x + 122.01, and to the 
trend for the yield per acre, y = . 1844a: +98. 57, the ori- 
gin, in the former case, being at 1875 and, in the latter, 



120 



Economic Cycles: Their Latv and Cause 













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The Mechanism of Cycles 



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122 Economic Cycles: Their Law and Cause 

at 1871.^ These two equations make it possible to 
eliminate the secular trends upon which move the 
cycles of prices and the cycles of yield. The results of 
the calculations are given in Table VII of the Appendix 
to this chapter. 

Figure 26 presents the cycles of yield per acre and the 
cycles of general prices after the secular trends upon 
which they were respectively superposed have been 
eliminated. It is quite evident, now, from the appear- 
ance of the graphs, that the cycles of yield per acre and 
the cj'^cles of general prices are closely related, and that 
the cycles of prices lag several years behind the cycles of 
crops. What is the amount of the lag and how closely 
are the cycles correlated? Both of these questions may 
be answered at once by following the method that was 
adopted to measure the lag in the cycles of pig-iron 
production. If the cycles of the yield per acre are 
correlated ^ with the cycles of general prices we find, for 
a lag of three years in general prices, r = .786; for a lag 
of four years, r = .800; for a lag of five years, r = .710. 
The cycles in the yield per acre of the crops are, there- 
fore, intimately connected with the cycles of general 
prices, and the lag in the cycles of general prices is 
approximately four years. 

Figure 27 presents the two series of cycles with the 
lag of four years in the cycles of prices eliminated. It is 

1 The first equation was computed from the data for 1875-1910, 
and the second equation, from the data for 1871-1906. 

^ The data for the calculation are given in columns 4 and 7 of 
Table VII in the Appendix to this chapter. 



The Mechanism of Cycles 



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124 Economic Cycles: Their Law and Cause 

surely not an exaggeration to say that the congruence of 
the two rhythmical movements of crop yield and general 
prices is so close as to justify the inference that the one 
series is the cause of the other. Every important 
rhythmical feature of the yield curve is reproduced in 
the price curve : the long cycle which in both curves dips 
below the horizontal between 1880 and 1900, and the 
smaller superposed cycles that move upon the large 
ground-swell. The one apparent exception occurs in 
the price movement between 1887 and 1891 in which 
the price curve does not keep close to the yield curve. 
But this is not a real exception. For, in the first place, 
the price curve is convex between these limits, that 
is to say, it shows a tendency to conform to the yield 
curve; and, in the second place, since in the price 
curve a lag of four years has been eliminated, the date 
at which the disturbance occurs is really four years 
later than would appear from the dates on the chart. 
That would place the disturbance at about 1893, which 
was the year of the panic with extraordinary condi- 
tions in the state of the currency and the money mar- 
ket. 

Considering the high correlation between the two 
series of cycles and the harmony of their congruence 
with the theory of economic cycles embodied in this 
Essay, we conclude that the cycles of the yield per 
acre of the crops cause the cycles of general prices and 
that the law of the cycles of crops is the law of the cycles 
of general prices. 



The Mechanism of Cycles 1 25 

The chief results of this chapter may be summarized 
in a few propositions : 

(1) The yield per acre, for the whole of the United 

States, of the four representative crops, corn, 
hay, oats, and potatoes is so closely correlated 
with the yield per acre of these crops in Illinois 
as to render it very probable that the cause of 
the cycles of the yield in the United States 
is the same as the cause of the cycles in Illinois. 
The meteorological cause of the rhythmical 
changes in the yield of Illinois has been dis- 
cussed in an earher chapter. 

(2) The prices in the United States of the four 

representative crops are as closely related to 
the yield per acre of the crops as the prices are 
related to the total supply of the respective 
crops. For the purpose of prediction of prices, 
therefore, the yield-price curve is as useful as 
the demand curve. 

(3) The curves representing the relation between the 

yield per acre and price, in case of the four 
representative crops, fall during a period of 
falling yield and falling general prices, and 
rise under the contrary circumstances. 

(4) The falling or rising yield per acre of the crops 

leads to a falling or rising volume of trade in 
producers' goods. If the production of pig- 
iron be taken as a representative producers' 
good, then 

(a) The deviations of the annual production 



126 Economic Cycles: Their Law and Cause 

of pig-iron from the general cyclical 
movement in the production of pig-iron 
are directly correlated with the devia- 
tions, in the preceding year, of the 
yield per acre of the crops from their 
general cyclical movement ; 
(b) When the lag in the production of pig- 
iron and the secular trend in both the 
production of pig-iron and in the yield 
per acre of the crops are eliminated, the 
cycles of production of pig-iron are very 
closely correlated with the cycles of the 
yield per acre of the crops. The coeffi- 
cient of correlation is r = .719. 

(5) UnUke the law of demand for the crops, the law of 

demand for a representative producers' good 
is such that as the supply increases the price 
rises, and as the supply decreases the price 
falls. 

(6) With the falhng of the yield per acre of the crops 

there is a falHng volume of trade, a falling 
price of producers' goods, an increase in un- 
employment, and a fall in the yield-price 
curves for the crops. The contrary conditions 
prevail under a rising yield per acre of the 
crops. 

(7) The ultimate effect upon general prices of the 

process described in (6) is that 

(a) The deviations of general prices from 
their general cycUcal movement are 



The Mechanism of Cycles 127 

directly correlated with the deviations 
of the yield per acre of the crops from 
their general cycUcal movement; 
(b) When the lag in general prices and the 
secular trend in both prices and yield 
per acre are eliminated, the cycles of 
general prices are very closely corre- 
lated with the cycles of the yield per 
acre of the crops. The coefficient of 
correlation is r = .800. 

(8) The law of the cycles of crops is the law of the 

cycles in the activity of industry and the 
law of the cycles of general prices. 

(9) The fundamental, persistent cause of the cycles 

in the activity of industry and of the cycles of 
general prices is the cychcal movement in the 
yield per acre of the crops. 



128 Economic Cycles: Their Law and Cause 



APPENDIX 



TABLE I. — Index Number of the Yield Per Acre of Crops 



Year 


Index for 
Nine Crops 


Index for 
Four Crops 


Year 


Index for 
Nine Crops 


Index for 
Four Crops 


1870 


108 


109 


1891 


108 


107 


1871 


105 


113 


1892 


98 


93 


1872 


110 


115 


1893 


92 


95 


1873 


99 


98 


1894 


90 


85 


1874 


88 


88 


1895 


102 


104 


1875 


110 


114 


1896 


102 


111 


1876 


98 


101 


1897 


102 


102 


1877 


106 


110 


1898 


111 


108 


1878 


109 


113 


1899 


105 


108 


1879 


111 


114 


1900 


104 


105 


1880 


106 


107 


1901 


89 


83 


1881 


82 


82 


1902 


114 


117 


1882 


100 


99 


1903 


107 


111 


1883 


97 


100 


1904 


114 


117 


1884 


101 


105 


1905 


116 


121 


1885 


98 


102 


1906 


119 


120 


1886 


93 


93 


1907 


106 


107 


1887 


89 


85 


1908 


109 


110 


1888 


100 


103 


1909 


108 


111 


1889 


104 


106 


1910 


109 


113 


1890 


89 


86 


1911 


99 


95 



The Mechanism of Cycles 



129 



TABLE II. — The General Cyclical Movement and the Dif- 
ferences OF THE Production of Pig-Iron in the United 

States 



Year 


Produc- 
tion OF 

PlG-IRON 

IN Thou- 
sands OF 
Long 
Tons 


The Gen- 
eral Cy- 
clical 
Move- 
ment 
(Progres- 
sive Av- 
erages of 
Three 
Years) 


Differ- 
ence Be- 
tween 
THE Ac- 
tual 
Produc- 
tion AND 
the Gen- 
eral Cy- 
clical 
Move- 
ment 


Year 


Produc- 
tion OP 
Pig-iron 
IN Thou- 
sands OF 
Long 
Tons 


The Gen- 
eral Cy- 
clical 
Move- 
ment 
(Progres- 
sive Av- 
erages OF 
Three 
Years) 


Differ- 
ence Be- I 
tweenthe 
Actual 
Produc- 
tion and 
THE Gen- 
eral Cy- 
clical 
Move- 
ment 


1870 


1,665 






1891 


8,280 


8,880 


— 600 


1871 


1,707 


1,974 




1892 


9,157 


8,187 


+ 970 


1872 


2,549 


2,272 


4-277 


1893 


7,125 


7,647 


— 522 


1873 


2,561 


2,504 


+ 57 


1894 


6,658 


7,743 


—1085 


1874 


2,401 


2,329 


+ 72 


1895 


9,446 


8,242 


+ 12J4 


1875 


2,024 


2,098 


— 74 


1896 


8,623 


9,241 


— 618 


187t) 


1,869 


1,987 


—118 


1897 


9,653 


10,017 


— 364 


1877 


2,067 


2,079 


— 12 


1898 


11,774 


11,683 


+ 91 


1878 


2,301 


2,370 


— 69 


1899 


13,621 


13,061 


+ 560 


1879 


2,742 


2,626 


+ 116 


1900 


13,789 


14,429 


— 640 


1880 


3,835 


3,574 


-f261 


1901 


15,878 


15,829 


+ 49 


1881 


4,144 


4,201 


— 57 


1902 


17,821 


17,236 


+ 585 


1882 


4,623 


4,454 


+ 169 


1903 


18,009 


17,442 


+ 567 


1883 


4,596 


4,439 


+ 157 


1904 


16,497 


19,166 


—2669 


1884 


4,098 


4,246 


—148 


1905 


22,992 


21,599 


+ 1393 


1885 


4,045 


4,609 


—564 


1908 


25,307 


21,693 


+ 614 


1886 


5,683 


5,382 


+301 


1907 


25,781 


22,341 


+3440 


1887 


6,417 


6,197 


+220 


1908 


15,936 


22,504 


—6568 


1888 


6,190 


6,837 


—347 


1909 


25,795 


23,012 


+2783 


1889 


7,604 


7,766 


—162 


1910 


27,304 


25,5S3 


+ 1721 


1890 


0,203 


8,362 


+841 


1911 


23,650 







130 Econo7nic Cycles: Their Law and Cause 



TABLE III. — The General Cyclical Movement and the Dif- 
ferences OF THE Index Number of the Yield Per Acre of 
Nine Crops 



Year 


Index of 

Yield 

Per 

Acre 

(Nine 
Crops) 


The Gen- 
eral Cy- 
clical 
Move- 
ment 
(Progres- 
sive Av- 
erages OF 
Three 
Years) 


Differ- 
ence Be- 
tween THE 

Actual 
Index and 
THE Gen- 
eral Cy- 
clical 
Move- 
ment 


Year 


Index of 
Yield 
Per 
Acre 

(Nine 
Crops) 


The Gen- 
eral Cy- 
clical 
Move- 
ment 
(Progres- 
sive Av- 
erages of 
Three 
Years) 


Differ- 
ence Be- 
tween the 

Actual 
Index and 
THE Gen- 
eral Cy- 
clical 
Move- 
ment 


1870 


108 






1891 


108 


98.3 


+ 9.7 


1871 


105 


107.7 


— 2.7 


1892 


98 


99.3 


— 1.3 


1872 


110 


104.7 


+ 5.3 


1893 


92 


93.3 


— 1.3 


1873 


99 


99.0 


0.0 


1894 


90 


94.7 


— 4.7 


1874 


88 


99.0 


—11.0 


1895 


102 


98.0 


+ 4.0 


1875 


110 


98.7 


+ 11.3 


1896 


102 


102.0 


0.0 


1876 


98 


104.7 


— 6.7 


1897 


102 


105.0 


— 3. a 


1877 


106 


104.3 


+ 1.7 


1898 


111 


106.0 


-f- 5.0 


1878 


109 


108.7 


+ .3 


1899 


105 


106.7 


— 1.7 


1879 


111 


108.7 


-f 2.3 


1900 


104 


99.3 


+ 4.7 


1880 


106 


99.7 


+ 6.3 


1901 


89 


102.3 


—13.3 


1881 


82 


96.0 


—14.0 


1902 


114 


103.3 


+ 10.7 


1882 


100 


93.0 


-f 7.0 


1903 


107 


111.7 


— 4.7 


1883 


97 


99.3 


— 2.3 


1904 


114 


112.3 


+ 1.7 


1884 


101 


98.7 


+ 2.3 


1905 


116 


116.3 


— .3 


1885 


98 


97.3 


+ .7 


1906 


119 


113.7 


+ 5.3 


1886 


93 


93.3 


— .3 


1907 


106 


111.3 


— 5.3 


1887 


89 


94.0 


— 5.0 


1908 


109 


107.7 


+ 1.3 


1888 


100 


97.7 


+ 2.3 


1909 


108 


108.7 


— .7 


1889 


104 


97.7 


+ 6.3 


1910 


109 


105.3 


+ 3.7 


1890 


89 


100.3 


—11.3 


1911 


99 







The Mechanism of Cycles 



131 



TABLE IV. — Cycles of Yield Per Acre of Crops and Cycles 
OF Production of Pig-iron 



Year 


General 
Cyclical 
Move- 
ment 
of Yield 
Per Acre 
OF Crops 


Ordinate 

OF THE 

Secular 
Trend 


Cycles 
OF Yield 
Per Acre 
OF Crops 


General 
Cyclical 
Movement 
OF Produc- 
tion OF Pig- 
iron, IN 
Thousands 
OF Tons 


Ordinate 
of the 

Secular 
Trend 


Cycles of 
Production 
of Pig-iron 


1871 


107.7 


98.6 


-f 9.1 


1,974 


— 1,546 


+3,520 


1872 


104.7 


98.8 


+ 5.9 


2,272 


— 964 


+3,236 


1873 


99.0 


98.9 


+ .1 


2,504 


— 381 


+2,885 


1874 


99.0 


99.1 


— .1 


2,329 


202 


+2,127 


1875 


98.7 


99.3 


— .4 


2,098 


784 


+ 1,314 


1876 


104.7 


99.5 


-1- 5.2 


1,987 


1,307 


+ 620 


1877 


104.3 


99.7 


+ 4.6 


2,079 


1,950 


+ 129 


1878 


108.7 


99.9 


+ 8.8 


2,370 


2,532 


— 162 


1879 


108.7 


100.0 


+ 8.7 


2,626 


3,115 


— 489 


1880 


99.7 


100.2 


— .5 


3,574 


3,698 


— 124 


1881 


96.0 


100.4 


— 4.4 


4,201 


4,281 


— 80 


1882 


93 


100.6 


— 7.6 


4,454 


4,863 


— 409 


1883 


99.3 


100.9 


— 1.6 


4,439 


5,446 


—1,007 


1884 


98.7 


101.0 


— 2.3 


4,246 


6,029 


—1,783 


1885 


97.3 


101.2 


— 3.9 


4,609 


6,611 


—2,002 


1886 


93.3 


101.3 


— 8.0 


5,382 


7,194 


—1,812 


1887 


94.0 


101.5 


— 7.5 


6,197 


7,777 


—1,580 


1888 


97.7 


101.7 


— 4.0 


6,837 


8,360 


—1,523 


1889 


97.7 


101.9 


— 4.2 


7,766 


8,942 


—1,176 


1890 


100.3 


102.1 


— 1.8 


8,362 


9,525 


—1,163 


1891 


98.3 


102.3 


— 4.0 


8,880 


10,108 


—1,228 


1892 


99.3 


102.4 


— 3.1 


8,187 


10,690 


—2,503 


1893 


93.3 


102.6 


— 9.3 


7,647 


11,273 


—3,626 


1894 


94.7 


102.8 


— 8.1 


7,743 


11,856 


—4,112 


1895 


98.0 


103.0 


— 5.0 


8,242 


12,439 


—4,197 


1896 


102.0 


103.2 


— 1.2 


9,241 


13,021 


—3,780 


1897 


105.0 


103.4 


+ 1.6 


10,017 


13,604 


—3,587 


1898 


106.0 


103 . 5 


+ 2.5 


11,683 


14,187 


—2,504 


1899 


106.7 


103.7 


+ 3.0 


13,061 


14,769 


— 1,708 


1900 


99.3 


103.9 


— 4.6 


14,429 


15,352 


— 923 


1901 


102.3 


104.1 


— 1.8 


15,829 


15,935 


— 106 


1902 


103.3 


104.3 


— 1.0 


17,236 


16,518 


+ 718 


1903 


111.7 


lOi.5 


+ 7.2 


17,442 


17,100 


+ 342 


1904 


112.3 


104.7 


+ 7.6 


19,166 


17,6S3 


+ 1,483 


1905 


116.3 


104.8 


+ 11.5 


21,599 


1S,2G6 


+3,3:yj 


1906 


113.7 


105.0 


+ 8.7 


24,693 


18,848 


+5,845 


1907 


111.3 


105.2 


+ 6.1 


22,341 


19,431 


+2,910 


1908 


107.7 


105.4 


+ 2.3 


22,504 


20,014 


+ 2,490 


1909 


108.7 


105.5 


+ 3.2 


23,012 


20,596 


+2,416 


1910 


105.3 


105.7 


— .4 


25,583 


21,179 


+4,404 



132 Economic Cycles: Their Law and Cause 



TABLE V. — Percentage Change in the Production of Pig- 
iron AND Mean Percentage Change in the Price of Pig-iron 





Percent- 

TAOE 


Percentage Change in the Price op Pig-iron 


Mean 
Percent- 










Year 


Change in 

THE PrO- 


No. 1 
Foundry 


Gray 

Forge at 


Gray 

Forge 


Bessemer 


age 
Change in 




ductio.v of 
Pig-iron 


AT Phila- 
delphia 


Philadel- 
phia 


Lake Ore 
AT Pitts- 
burg 


at 
Pittsburg 


Price of 
Pig-iro.n 


1870 














1871 


+ 2.52 


+ 5.57 








+ 5.57 


1872 


+49.33 


+39.51 








+39.51 


1873 


+ .47 


—12.57 








—12.57 


1874 


— 6.25 


—29.45 




—24.13 




—26.79 


1875 


—15.70 


—15.44 




—12.85 




—14.14 


1876 


— 7.66 


—13.08 




— 8.15 




—10.61 


1877 


+ 10.59 


—14.74 




— 5.24 




— 9.99 


1878 


+ 11.32 


— 6.61 




—12.18 




— 9.39 


1879 


+ 19.17 


+22.92 




+22.44 




+22.68 


1880 


+39.86 


+31.12 




+26.32 




+28.72 


1881 


+ 8.06 


—11.62 




—18.01 




—14.82 


1882 


+ 11.56 


+ 2.38 




+ 3.92 




+ 3.15 


1883 


— .58 


—13.00 


—14.47 


—20.13 




—15.87 


1884 


—10.84 


—11.64 


— 8.38 


— 9.82 




— 9.95 


1885 


— 1.29 


— 9.14 


—12.03 


—11.07 




—10.75 


1886 


+41.61 


+ 4.00 


+ 5.26 


+ 8.58 




+ 5.95 


1887 


+ 12.92 


+ 11.87 


+ 8.48 


+ 14.72 


+ 12.71 


+ 11.95 


1888 


+ 1.14 


— 9.79 


— 8.88 


—15.93 


—18.67 


—13.32 


1889 


+ 17.16 


— 5.93 


— 4.50 


— 4.00 


+ 3.57 


— 2.72 


1890 


+21.03 


+ 3.66 


+ 2.20 


+ 2.80 


+ 4.83 


+ 3.37 


1891 


—10.03 


— 4.83 


— 8.22 


—10.90 


—15.47 


— 9.85 


1892 


+ 10.59 


—10.10 


— 6.75 


— 8.89 


— 9.91 


— 8.91 


1893 


—22.19 


— 7.81 


— 5.98 


— 8.12 


—10.44 


— 8.09 


1894 


— 6.55 


—12.81 


—15.71 


—17.16 


—11.58 


—14.32 


1895 


+41.87 


+ 3.48 


+ 7.08 


+ 12.21 


+ 11.78 


+ 8.64 


1896 


— 8.71 


— 1.15 


— 3.48 


— 5.03 


— 4.56 


— 3.55 


1897 


+ 11.94 


— 6.56 


— 5.50 


—13.09 


—16.56 


—10.43 


1898 


+21.97 


— 3.64 


— 2.39 


+ 1.66 


+ 1.97 


— .60 


1899 


+ 15.70 


+66.04 


+62.27 


+82.14 


+84.22 


+73.67 


1900 


+ 1.23 


+ 3.20 


— .66 


+ 1.08 


+ 2.42 


+ 1.51 


1901 


+ 15.15 


—20.57 


—14.61 


—15.98 


—18.27 


—17.36 


1902 


+ 12.24 


+39.82 


+36.36 


+37.25 +29.76 1 


+35.80 


1903 


+ 1.05 


—10.23 


—10.78 


—10.11 


— 8.18 


—10.07 


1904 


— 8.40 


—21.84 


—20.20 


—26.43 


—27.50 


—23.99 


1905 


+39.37 


+ 14.84 


+ 13.97 


+21.18 


+ 18.90 


+ 17.22 


1906 


+ 10.07 


+ 17.34 


+ 14.18 


+ 16.45 


+ 19.44 


+ 16.85 


1907 


+ 1.87 


+ 13.87 


+ 18.38 


+ 18.31 


+ 16.89 


+ 16.86 


1908 


—38.19 


—25 91 


—25.36 


—29.23 


—25.26 


—26.44 


1909 


+61.87 


+ .62 


+ 2.61 


+ 2.10 


+ 1.99 


+ 1.83 


1910 


+ 5.85 


— 2.53 


— 2.54 


— 1.99 


— 1.26 


— 2.08 


1911 


—13.38 


— 9.50 


— 8.21 


— 8.33 


— 8.61 


— 8.66 


1912 


+25.70 


+ 5.41 


+ 6.65 


+ 4.08 


+ 1.40 


+ 4.40 



The Mechanism of Cycles 



133 



TABLE VI. — The Index Number of General Prices. 
General Cyclical Movement and its Differences 



Its 



Year 


Falkner's 
Index of 
Prices of 
"All Ar- 
ticles" 


Bureau of 
Labor's 
Inde.x of 
Prices of 
" .\ll Com- 
.modities" 


Falkner's 
Index 

Adjusted 
to the 
Base op 

THE Bur- 
eau OF 
Labor 


The Con- 
tinuous 

Inde.x of 
Price.s 


General 

Cyclical 

[ move.me.ni 

of the 
j Continu- 
1 ous Inde.x 
1 OF Prices 
1 


Difference 
Between 

THE Actual! 

Index and 
THE Gen- 
eral Cy- 
clical 

Movement 


1870 


117.3 




143.5 


143.5 






1871 


122.9 




150.3 


150.3 


149. S 


+ .3 


1872 


127.2 




155.6 


155.6 


151.7 


-1-3.9 


1873 


122.0 




149.2 


149.2 


150.3 


—1.1 


1874 


119.4 




146.0 


146.0 


144.6 


+ 1.4 


1875 


113.4 




138.7 


138.7 


137.6 


+ 1.1 


1876 


104.8 




128.2 


128.2 


131.5 


—3.3 


1877 


104.4 




127.7 


127.7 


126.0 


+ 1.7 


1878 


99.9 




122.2 


122.2 


122.7 


— .5 


1879 


96.6 




118.2 


118.2 


123.7 


—5.5 


1880 


106.9 




130.8 


130.8 


126.1 


+4.7 


1881 


105.7 




129.3 


129.3 


130.9 


—1.6 


1882 


108.5 




132.7 


132.7 


130.6 


+2.1 


1883 


106.0 




129.7 


129.7 


128.0 


+ 1.7 


1884 


99.4 




121.6 


121.6 


121.7 


— .1 


1885 


93.0 




113.8 


113.8 


115.9 


—2.1 


1886 


91.9 




112.4 


112.4 


113.2 


— .8 


1887 


92.6 




113.3 


113.3 


113.6 


— .3 


1888 


94.2 




115.2 


115.2 


114.6 


+ .6 


1889 


94.2 




115.2 


115.2 


114.4 


+ .8 


1890 


92.3 


112.9 




112.9 


113.3 


— .4 


1891 




111.7 




111.7 


110.2 


+ 1.5 


1892 




106.1 




106.1 


107.8 


—1.7 


1893 




105.6 




105.6 


102.6 


+3.0 


1894 




96.1 




96.1 


98.4 


—2.3 


1895 




93.6 




93.6 


93.4 


+ .2 


1896 




90.4 




90.4 


91.2 


— .8 I 


1897 




89.7 




89.7 


91.2 


—1.5 


1898 




93.4 




93.4 


94.9 


—1.5 


1899 




101.7 




101.7 


101.9 1 


— .2 


1900 




110.5 




110.5 


108.9 


+3.6 


1901 




108.5 




108.5 


110.6 


—2.1 


1902 




112.9 




112.9 


111.7 


+ 1.2 1 


1903 




113.6 




113.6 


113.2 


+ -4 1 


1904 




113.0 




113.0 


114.2 


—1.2 


1905 




115.9 




115.9 


117.1 


—1.2 


1906 




122.5 




122.5 


122.6 


— .1 


1907 




129.5 




129.5 


124.9 


+4 6 


1908 




122.8 




122.8- 


126.3 


—3.5 


1909 




126.5 




126.5 


127.0 


— .5 


1910 




131.6 




131.6 


129.1 


+2.5 


1911 




129.3 




129.3 




1 



134 Economic Cycles: Their Law and Cause 



TABLE VII. — Cycles of Yield Per Acre op Crops and Cycles 
OF General Prices 



Year 


General 
Cyclical 

Move- 
ment OF 
Yield Per 
Acre of 

Crops 


Ordinates 

OP the 

Secular 

Trend 


Cycles of 
the Yield 
Per Acre 
of Crops 


General 
Cyclical 

Move- 
ment OF 
General 

Prices 


Ordinates 

OP THE 

Secular 
Trend 


Cycles of 

General 

Prices 


1871 


107.7 


98.6 


+ 9.1 


149.8 


123.5 


+26.3 


1872 


104.7 


98.8 


+ 5.9 


151.7 


123 . 1 


+28.6 


1873 


99.0 


98.9 


+ .1 


150.3 


122.8 


+27.5 


1874 


99.0 


99.1 


— .1 


144.6 


122.4 


+22.2 


1875 


98.7 


99.3 


— .4 


137.6 


122.0 


+ 15.6 


1876 


104.7 


99.5 


+ 5.2 


131.5 


121.6 


+ 9.9 


1877 


104.3 


99.7 


+ 4.6 


126.0 


121.3 


+ 4.7 


1878 


108.7 


99.9 


+ 8.8 


122.7 


120.9 


+ 1.8 


1879 


108.7 


100.0 


+ 8.7 


123.7 


120.5 


+ 3.2 


1880 


99.7 


100.2 


— .5 


126.1 


120.2 


+ 5.9 


1881 


96.0 


100.4 


— 4.4 


130.9 


119.8 


+ 11.1 


1882 


93.0 


100.6 


— 7.6 


130.6 


119.4 


+ 11.2 


1883 


99.3 


100.9 


— 1.6 


128.0 


119.0 


+ 9.0 


1884 


98.7 


101.0 


— 2.3 


121.7 


118.7 


+ 3.0 


1885 


97.3 


101.2 


— 3.9 


115.9 


118.3 


— 2.4 


1886 


93.3 


101.3 


— 8.0 


113.2 


117.9 


— 4.7 


1887 


94.0 


101.5 


— 7.5 


113.6 


117.6 


— 4.0 


1888 


97.7 


101.7 


— 4.0 


114.6 


117.2 


— 2.6 


1889 


97.7 


101.9 


— 4.2 


114.4 


116.8 


— 2.4 


1890 


100.3 


102.1 


— 1.8 


113.3 


116.5 


— 3.2 


1891 


98.3 


102.3 


— 4.0 


110.2 


116.1 


— 5.9 


1892 


99.3 


102.4 


— 3.1 


107.8 


115.7 


— 7.9 


1893 


93.3 


102.6 


— 9.3 


102.6 


115.3 


—12.7 


1894 


94.7 


102.8 


— 8.1 


98.4 


115.0 


—16.6 


1895 


98.0 


103.0 


— 5.0 


93.4 


114.6 


—21.2 


1896 


102.0 


103.2 


— 1.2 


91.2 


114.2 


—23.0 


1897 


105.0 


103.4 


4- 1.6 


91.2 


113.9 


—22.7 


1898 


106.0 


103.5 


+ 2.5 


94.9 


113.5 


—18.6 


1899 


106.7 


103.7 


+ 3.0 


101.9 


113.1 


—11.2 


1900 


99.3 


103.9 


— 4.6 


106.9 


112.8 


— 5.9 


1901 


102.3 


104.1 


— 1.8 


110.6 


112.4 


— 1.8 


1902 


103.3 


104.3 


— 1.0 


111.7 


112.0 


— .3 


1903 


111.7 


104.5 


+ 7.2 


113.2 


111.6 


+ 1.6 


1904 


112.3 


104.7 


+ 7.6 


114.2 


111.3 


+ 2.9 


1905 


116.3 


104.8 


+ 11.5 


117.1 


110.9 


+ 6.2 


1906 


113,7 


105.0 


+ 8.7 


122.6 


110.5 


+ 12.1 


1907 


111.3 


105.2 


+ 6.1 


124.9 


110.2 


+ 14.7 


1908 


107.7 


105.4 


+ 2.3 


126.3 


109.8 


+ 16.5 


1909 


108.7 


105.5 


+ 3.2 


127.0 


109.4 


+ 17.6 


1910 


105.3 


105.7 


— .4 


129.1 


109.0 


+23.1 



CHAPTER VI 

SUMMARY AND CONCLUSIONS 

These cycles of crops constitute the natural, material current 
which drags upon its surface the lagging, rhythmically changing 
values and prices with which the economist is more immediately 
concerned. 

The principal contribution of this Essay is the dis- 
covery of the law and cause of Economic Cycles. The 
rhythm in the activity of economic life, the alternation 
of buoyant, purposeful expansion with aimless depres- 
sion, is caused by the rhythm in the yield per acre of 
the crops; while the rhythm in the production of the 
crops is, in turn, caused by the rhythm of changing 
weather which is represented by the cyclical changes in 
the amount of rainfall. The law of the cycles of rainfall 
is the law of the cycles of the crops and the law of 
Economic Cycles. 

We shall recapitulate the main stages by which this 
conclusion was reached and shall take occasion, as the 
stages are reviewed, to suggest the care that must 
be observed in interpreting the statistical generaliza- 
tions which form the structure of the argument. 

When we begin to think seriously about the cause of 
Economic Cycles we are greatly impressed by the wide 
diffusion of these cyclical movements among the peoples 
of the world, and the inference appears to be inevitable 
that there must be some physical cause at work to 

135 



136 Economic Cycles: Their Law and Cause 

account for so general a movement. As the most 
fundamental need of mankind is the need for food, it 
seems probable that the observed rhythmical economic 
changes may be produced by the physical cause through 
its effect upon the food supply. If this be so, then, as 
the fluctuations of the food supply are known to be 
subject to the supposed caprices of the weather, it 
seems not unlikely that the physical cause may be one 
or more of the elemental forces that are summarized 
under the term weather. The variation in the quantity 
of the rainfall is one of the weather changes known to 
have a marked effect upon the yield of the crops, and 
if this fact is taken into consideration with the preceding 
reasoning, we have a working theory as to the cause of 
Economic Cycles: The changes in the weather repre- 
sented by the changes in the quantity of rainfall cause 
the changes in the yield per acre of the crops, and the 
variation^ in the yield of the crops cause the economic 
changes known as Economic Cycles. With this work- 
ing theory in mind, we examined appropriate data with 
reference to three things: (1) The periodicity of rain- 
fall; (2) the effect of rainfall on the crops; (3) the rela- 
tion of the yield of the crops to Economic Cycles. 

First, then, as to the periodicity of rainfall. The 
problem as to whether the quantity of rainfall passes 
through definite cycles involves two practical questions 
that affect the utility and the validity of the results that 
may be attained. These questions are, first, as to what 
rainfall data shall be used in the investigation of possible 
rainfall cycles; and, second, as to the method that shall 



Summary and Conclusions 137 

be adopted to establish the existence of the cycles and 
to ascertain their characteristic lengths, amplitudes and 
phases. In our investigation, the choice of rainfall data 
was suggested by the scope of our general problem. 
Supposing that we could find definite periods in the 
varying amount of the rainfall, we should then desire to 
know the relation of rainfall to the yield of the crops, 
and the relation of the yield of the crops to Economic 
Cycles. It was necessary, therefore, that the data 
of rainfall should refer to an area in which important 
crops are produced, and it was desirable that the data of 
both rainfall and crops should refer to a highly dynamic 
society. For these reasons we collected the material 
for our investigation from the central part of the United 
States. 

The method adopted in an investigation of the 
periodicity of rainfall must satisfy three conditions: 
(1) It must exhaust the data in the search for possible 
cycles; that is to say, the data must be made to yield 
all the truth they contain relating to the particular 
problem in hand. Frequently in the past, spurious 
periodicities have been presented as real periodicities, 
chiefly because the investigator started with a bias in 
favor of a particular period and did not pursue his 
researches sufficiently far to determine whether his 
result was not one among many spurious, chance 
periodicities contained in his material. In the search for 
real periodicities the data must be exhaustively ana- 
lyzed. (2) The method must render possible the dis- 
crimination between a true periodicity, having its 



138 Economic Cycles: Their Law and Cause 

origin in a natural cause and persisting with a change in 
the samples of statistics, and a spurious periodicity 
which is purely formal, having its origin in accidental 
characteristics of the statistical sample and disappear- 
ing, or radically altering its character, when different 
samples of statistics are made the basis of the computa- 
tion. (3) The method must not only make possible 
the isolation of real periodicities, but it must likewise 
enable one to determine their essential characteristics, 
their length, phases and amplitudes. The method we 
adopted in our researches, which is based upon the 
harmonic analysis, satisfies these three conditions. 

The result of our investigation as to the periodicity of 
rainfall in the upper Mississippi Valley was the dis- 
covery that the annual rainfall passes through two 
cycles of approximately thirty-three years and eight 
years in length. The amplitude and phases of these 
two cycles were ascertained, and the equations to the 
separate cycles were calculated. The two cycles were 
then superposed, thus giving the general cyclical move- 
ment of rainfall; the equation of this compound cycle 
was computed and the graph was drawn. It was found 
that the curve of the rhythmical movement of rainfall 
computed from the equation to the superposed cycles 
fitted excellently well the actual observations of rainfall. 
These results constitute the solution of the first part of 
our general problem : Rainfall in the principal crop area 
of the United States passes through cycles of thirty- 
three years and of eight years. 

The caution that should be observed in the use of our 



Summary and Conclusions 139 

conclusions is suggested by the method that was em- 
ployed and the subject that was investigated. The 
inquiry is a statistical study of an aspect of meteorology, 
and, therefore, the caution to be exercised in the use 
of the conclusions is the caution that should be applied 
to statistical work in general and to meteorology in 
particular. As far as the statistical work is concerned, 
it should be observed that the data were drawn from a 
limited area of the United States and covered, at most, 
seventy- tw^o years. Consequently, while there seem to 
be very good reasons in favor of the belief that, for the 
purpose for which they were used, the data were repre- 
sentative of the whole country, it is highly desirable 
that similar studies should be made for other places and 
other times. Furthermore, the present investigation 
was limited to a study of the periodicity of rainfall, but 
a more adequate research would embrace the periodicity 
of temperature and of other weather elements, together 
with an investigation of the interrelation of the elements. 
Before passing on to consider the caution to be observed 
in the use of statistical studies of meteorology, a word 
should be said in justification of the limitation of the 
inquiry to the periodicity of annual rainfall. The ob- 
ject of taking annual rainfall was to ascertain the mean 
periodicity of the rainfall of the critical seasons of the 
several crops. It would have been more satisfactory to 
investigate the periodicity of the rainfall of the critical 
season in case of each crop, but, because of the extreme 
laboriousness of the calculations, a device had to be 
adopted to limit the amount of computation. 



140 Economic Cycles: Their Law and Cause 

In regard to the use of statistical generalizations in 
meteorology, we have the cautious opinion of Lord 
Kelvin: ''I cannot say whether anything with reference 
to Terrestrial Meteorology is done once for all. I 
think probably the work will never be done." There 
is always need of checking up statistical conclusions in 
the light of new data, and this necessity applies to the 
generaUzation that in the Mississippi Valley the annual 
rainfall passes through a double cycle of thirty-three 
years and eight years. This conclusion is undoubtedly 
warranted by the data that lie at the basis of the in- 
vestigation, but it would be a grave fault, indeed, to 
hold that the cycles do not alter with the flow of time. 
Whether they change or retain their characteristics can 
be determined only by accumulating more data than 
are at present available. 

We come now to the second part of our general 
problem, namely, to the consideration of the relation 
between rainfall and the yield of the crops, and again 
the questions of data and method must be settled. 
In choosing the data, the prime consideration was to 
make sure that the crops selected should be representa- 
tive of the conditions of crop-producing in the Middle 
West. The five principal crops in the Middle West are 
corn, hay, wheat, oats, and potatoes, and of these five 
all except wheat were taken to serve as representative 
crops. Wheat was omitted because of technical dif- 
ficulties : First, it is impossible, except for recent years, 
to separate in the published statistics the yield per acre 



Summary and Conclusions 141 

of spring wheat from the yield of winter wheat; and, 
secondly, since the growth seasons and critical periods 
of these two varieties of wheat are different, it seemed 
unwise to attempt to connect the rainfall of any season 
with the yield per acre of wheat in which the figures for 
the yield referred to spring and winter wheat taken 
together. For these reasons the representative crops 
were limited to corn, hay, oats, and potatoes; and the 
yield per acre of these several crops throughout a long 
period of time, together with the rainfall of their 
respective criticat seasons, form the numerical data of 
the investigation. 

The method of determining the critical seasons was to 
find, by the use of the statistical theory of correlation, 
the month or months, in the Hfetime of the several 
crops, the rainfall of which gave the highest correlation 
with the ultunate yield. This preliminary inquiry 
afforded a partial answer to our general question as to 
the relation between rainfall and the crops. We found 
that in case of each of the crops the yield per acre is 
directly connected with the rainfall of some critical 
period, and in all of the crops except oats the connection 
is very close. It seemed probable, therefore, that since 
the rainfall passes through definite cycles, and since 
the yield per acre of the crops is intimately related with 
the rainfall of their respective critical seasons, the yield 
per acre of the crops should hkewise pass through the 
double cycle described by the rainfall of the critical 
seasons. 

The investigation of the relation of the cycles of the 



142 Economic Cycles: Their Law and Cause 

crops to the cycles of the rainfall of the critical seasons 
was carried out in two ways, first for the crops taken 
singly, and then for the crops taken all together. In the 
inquiry relating to the separate crops, the equations to 
the double cycle in the yield per acre and to the double 
cycle in the rainfall of the corresponding critical seasons 
were computed, and the graphs were drawn. When the 
graphs of the cycles of the crops were superposed upon 
the graphs of the cycles of rainfall of the respective 
critical seasons, the two curves were found to present a 
very remarkable congruence. In the inquiry relating 
to the crops taken all together, an index number of the 
yield per acre of the crops and an index number of the 
mean effective rainfall of the critical seasons were con- 
structed. The equations to the double cycle in both 
indices were computed, their graphs were drawn and 
then superposed. It was found that the characteristic 
features of the rainfall curve were reproduced in the 
curve of the index number of the yield per acre of the 
crops. 

These results, referring both to the crops taken singly 
and to the crops taken all together, are the answers to 
the second part of our general question: The yield per 
acre of the representative crops is closely connected 
statistically with the rainfall of the respective critical 
seasons, and the relation is so close that the cycles of 
the yield per acre of the crops reproduce in char- 
acteristic ways the cycles of the rainfall of the critical 
seasons. The fundamental, persistent cause of the 
cycles of crops is, therefore, the rhythmical movement 



Summary and Conclusions 143 

in the conditions of the weather represented by the 
cycles in the amount of rainfall. 

In the cautious use of the preceding generalizations, 
one will bear in mind that only four crops have been 
investigated, and that, in ascertaining the critical 
seasons, the monthly rainfall has been used. The 
critical seaons could undoubtedly be determined more 
accurately if the figures for the weekly rainfall were 
employed. Furthermore, the inquiry has been limited 
to the relation of the yield of the crops to rainfall, 
whereas a more adequate study would include at least 
the effects of temperature. 

Thus far the investigation has established the law 
and cause of the cycles of the crops: The cause of the 
cycles in the physical productivity of the crops is the 
cyclical variation of the weather represented by the 
cycles of rainfall, and the law of the cycles of rainfall is 
the law of the cycles of the crops. In order to bring 
these physical results into relation with the rhythmical 
movements of prices and values, we had first to show 
how the prices of the several crops vary with their 
respective supplies. In technical terms, we had to 
discover the laws of demand for the individual crops. 

The equations to the law of demand for corn, hay, 
oats, and potatoes were computed, and the graphs were 
drawn. The degree of precision with which these 
demand curves might be used as formulae for predicting 
prices was ascertained, and the coeflficients of the 
elasticity of demand for the representative commodities 



144 Economic Cycles: Their Law and Cause 

were calculated. The equations to the law of demand 
for all four crops conformed to a single type, indicating 
that as the supply of the commodity increases, the price 
falls. For reasons that were explained in the discussion, 
we named this type of demand curve the negative type. 

It will be recalled that the three divisions of our 
general problem were (1) the periodicity of rainfall; 
(2) the effect of rainfall upon the crops; and (3) the 
relation of the yield of the crops to Economic Cycles. 
The elaboration of a method for calculating the demand 
curves placed us in position to examine the third and 
final part of the problem. The law of demand for the 
crops connects the price of the several crops with their 
respective supplies, but the supply is dependent upon 
both the yield per acre and the extent of the acreage. 
In order to bring our findings with regard to the period- 
icity in the yield per acre into relation with prices and 
values, it is clear that we must know the relation 
between the variation in the price of the commodity 
and the yield per acre of the commodity. This ques- 
tion we examined at length, and found the tie between 
price and yield per acre to be as close as the tie between 
price and supply. To differentiate between demand 
curves and curves showing the relation between yield 
per acre and price, we called the latter curves, yield- 
price curves. We deduced the equations to the yield- 
price curves for the four representative commodities 
and measured the degree of precision with which their 
equations might be used as formulae for predicting 



Summary and Conclusions 145 

prices. In all of these relations, the yield-price curves 
were found to be as accurate and as satisfactory as 
the demand curves themselves. 

With the possession of the yield-price curves, showing 
the relation between the prices of the crops and their 
varying yield per acre, it might seem that the problem 
of agricultural cycles at least was completely elucidated. 
As we know how the periodicity in the yield of the crops 
follows upon the periodicity in the rainfall, and how the 
prices vary with the yield, one might conclude that 
the course of prices could be predicted for a long time. 
The inference would be entirely true but for the fact 
that the demand curves and the yield-price curves move 
alternately up and down with the flow of time. This 
complication made it necessary to investigate the 
rhythmical movement of the yield-price curves, and 
we found that the demand curves, or yield-price curves, 
rise or fall with the level of general prices and with the 
level of the index of the yield per acre of the crops. 

The preceding facts seemed to involve a contradiction 
with an a priori doctrine of theoretical economics. 
According to the economic dogma of the uniformity of 
the demand function, all demand curves are of the 
negative type: As the amount of the commodity in- 
creases, the price falls. But if this be true, how is it 
possible for a fall of general prices to accompany a fall 
in the index of the yield per acre of the crops? If the 
yield per acre of the crops decreases, then, according to 
the yield-price curves and the demand curves, the price 
of the crops will rise. Moreover, as the profits of trade 



146 Economic Cycles: Their Law and Cause 

and commerce are largely dependent upon the volume 
of the crops, it seems likely that the demand for general 
commodities would decrease with a deficiency in the 
harvests, and, according to the dogma of the uniformity 
of the demand function, the prices of general commodi- 
ties should rise. The ultimate result of bad harvests, 
therefore, would be a rise in general prices. The facts, 
however, bear out the contrary view. General prices 
fall with a decrease in the yield per acre of the crops. 
A consideration of this difficulty led to the discovery 
that there is a positive type of demand curve as well as a 
negative type. For a representative producer's good, 
for example pig-iron, the law of demand is such that as 
the amount of commodity increases the price of the 
commodity rises, and as the amount of the commodity 
decreases the price of the commodity falls. The exist- 
ence of both positive and negative types of demand in a 
highly dynamic society suggested a working theory 
which seemed to account for the interrelation of all 
the known relevant facts, and which may be stated in 
compact form. The rhythmically varying yield per 
acre of the crops is the cause of Economic Cycles: 
When the yield increases,' the volume of trade, the 
activity of industry and the amount of employment 
increase ; the demand for producers' goods increases and 
the prices of producers' goods rise; the demand curves 
for agricultural commodities rise; with the ultimate 
result of a rise of general prices. The contrary changes 
would follow upon a fall in the yield per acre of the 
crops. 



Summary and Conclusions 147 

Beyond what we had aheady estabhshed, this theory 
of the mterrelation of economic changes required for 
its complete demonstration the proof of the existence of 
two fundamental relations, to wit, that the cycles in the 
yield per acre of the crops are reproduced 

(1) in the activity of general industry; 

(2) in the movement of general prices. 

In order to test whether these relations actually exist, 
an index number of the yield per acre of the crops was 
constructed for the nine crops, corn, wheat, oats, barley, 
rye, buckwheat, hay, cotton, and potatoes. To make 
sure of keeping close to the results already established 
for the representative commodities corn, hay, oats, and 
potatoes, the correlation of the- index of the nine crops 
with the index of the four representative crops was 
computed and found to be r = .960. 

As the production of pig-iron is generally regarded as 
a good "barometer" of the activity of industry, we 
sought an answer to the above first question by in- 
vestigating whether the cycles in the yield per acre of 
the nine crops were reproduced in the cycles in the 
production of pig-iron. The inquiry involved the 
problems of the separation of the cycHcal and the secular 
movements in the production of pig-iron, and the 
ascertainment of the amount of the lag in the cycles 
of pig-iron behind the cycles in the yield per acre of the 
crops. We found that it takes between one and two 
years for the stimulation of increasing harvests to work 
out its maximum effect in promoting the activity of 
industry as that activity is represented in the ''barom- 



148 Economic Cycles: Their Law and Cause 

eter" of industry, the production of pig-iron; and 
that, when an allowance is made for a lag of two years 
in the adjustment of the pig-iron industry, the cycles 
of the yield per acre of the crops are generally repro- 
duced in the cycles of the production of pig-iron, the 
relation being so close that the coefficient of correlation 
is r = .718. 

To find the relation of the cycles in the yield per acre 
of the crops to the cycles in the movement of general 
prices, we made use of an index number of general 
prices extending from 1870 to 1910, and of our index 
number of the yield per acre of nine crops covering the 
same interval of time. The problem of separating the 
cyclical movements in these two series from their 
secular movements was solved, and the lag of the cycles 
of general prices behind the cycles in the yield of crops 
was found to be about four years. The coefficient of 
correlation between the cycles in the yield of the crops 
and the cycles in the general prices lagging four years 
behind the crop cycles reached the very high value 
r = .800. When the lagging cycles of general prices were 
plotted and their graph superposed upon the graph of 
the cycles in the yield per acre of the crops, the two 
curves were found to present a degree of congruence so 
close as to justify our working theory that the fun- 
damental, persistent cause of the cycles of prices is the 
rhythmical movement in the yield per acre of the crops. 
The cycles in the yield per acre of the crops are followed 
at an interval of about two years by the cycles in the 



Summary and Conclusions 149 

activity of industry and of the volume of trade, and at 
an interval of about four years in the cycles of prices. 
These conclusions brought to a close the last part of 
our general problem of the cause and law of Economic 
Cycles. 

The hnks in the sequence of causation were com- 
pletely established: The fundamental, persistent cause 
of the cycles in the yield of the crops is the cyclical 
movement in the weather conditions represented by the 
rhythmically changing amount of rainfall; the cyclical 
movement in the yield of the crops is the fundamental, 
persistent cause of Economic Cycles. 

In the Introduction to this Essay it was observed that 
economic dynamics stands in need of a law that shall 
be to a changing society what the law of diminishing 
returns is to a society in a relatively static state. We 
may now formulate the law: The weather conditions 
represented by the rainfall in the central part of the 
United States, and probably in other continental areas, 
pass through cycles of approximately thirty-three years 
and eight years in duration, causing like cycles in the 
yield per acre of the crops; these cycles of crops con- 
stitute the natural, material current which drags upon 
its surface the lagging, rhythmically changing values 
and prices with which the economist is more immedi- 
ately concerned. 



^T^HE following pages contain advertisements of Mac- 
-*- millan books by the same author. 



LAWS OF WAGES 

AN ESSAY IN STATISTICAL ECONOMICS 

By Henry Ludwell Moore 

Professor of Political Economy in 
Columbia University 

Cloth, il.60, net. 

Extract from the Introduction: " In the following chapters 
I have endeavored to use the newer statistical methods and 
the more recent economic theory to extract, from data re- 
lating to wages, either new truth or else truth in such new 
form as will admit of its being brought into fruitful relations 
with the generaUzations of economic science." 

CONTENTS 

PAGE 

Introduction 1 

Chapter I 

Statistical Laws 

A Scatter Diagram 11 

Definition of Terms 15 

Characteristics of Statistical Laws 21 

Chapter II 

Wages, Means of Subsistence, and the Standard of Life 

Description of Data 26 

Wages and the Means of Subsistence 29 

Wages and the Standard of Life 33 

Wages of Skilled and of Unskilled Laborers 39 

Chapter III 

Wages and the Productivity of Labor 

Description of Data 45 

Fluctuations in the Rate of Wages and in the Value of the Product 46 

(over) 



LAWS OF WAGES by Henry Ludwell Moore— Continued 

CONTENTS— Cow^mwed page 

Fluctuations in the Laborer's Relative Share of the Product and in 

the Ratio of Capital to Labor 55 

The General Trend of Wages 61 

Chapter IV 

Wages and Ability 

An Hypothesis as to the Distribution of AbiUty 74 

Grounds for the Hypothesis 76 

The Expression of the Gaussian Law in a Form that will facilitate 

the Testing of the Differential Theory of Wages 78 

The Standard Population 82 

The AppUcation of the Theory of the Standard Population 85 

Remark upon the Preceding Demonstration . . . , 93 

Chapter V 

Wages and Strikes 

Outcome of Strikes as affected by the Strength of Trades-Unions 105 

Outcome of Strikes as limited by Economic Law 121 

Summary 134 

Chapter VI 

Wages and the Concentration of Industry 

Wages as affected by the Concentration of Industry 140 

Amount of Employment 153 

Continuity of Employment 156 

Length of Working Day 161 

Chapter VII 

Conclusions 

Statistical Economics and Industrial Legislation 169 

Practical Aspects of the Results of Preceding Chapters 174 

Statistical Economics and Synthetic Economics 196 

COMMENTS OF SPECIALISTS 

"Professor Moore brings to his task a wide acquaintance with the 
most difficult parts of the literature of economics and statistics, a full 
appreciation of its large problems, a judicial spirit and a dignified style." 
F. W. Taussig, in the Quarterly Journal of Economics. 

"Statistics of the ordinary official kind have often served to support 
the arguments of political economists. But this is the first time, we 
believe, that the higher statistics, which are founded on the Calculus of 



LAWS OF WAGES by Henry Ludwell Moore— Continued 

Probabilities, have been used on a large scale as a buttress of economic 
theory." F. Y. Edgeworth, in the Economic Journal. 



"Professor Moore has broken new ground in a most interesting field, 
and while we may differ from him in the wciglit to be attached to this 
or that result or the interpretation to be placed on some observed co- 
efficient, we may offer cordial congratulations on the work as a whole. 
G. U. Yule, in the Journal of the Royal Statistical Society. 

"Die Fruchtbarkeit der verwendeten Methode scheint mir durch 
diese Untersuchungen zweifellos erwiesen, ebenso wie die Erreichbarkeit 
des Ziels, die Theorie ganz dicht an die Zahlenausdriicke der wirtschaft- 
hchen Tatsachen heranzubringen. Und das ist cine Tat, zu der der Autor 
nur zu begliickwunschen ist. . . . Hat das Buch auch auf der Hand 
liegende Fehler — in der Zukunft wird man sich seiner als der erstcn 
klaren, einfachen und zielbewussten Darlegung mid Exemphfizierung der 
Anwendung der 'hoheren Statistik' auf okonomische Frobleme dankbar 
erinnern." Joseph Schumpeter, in the Archiv fur Sozialwissenschaft 
und Sozialpolitik. 

"Non seulement il nous enseigne I'emploi d'une methode qui dans de 
certaines hmites peut etre tres f^conde. Mais encore son habilet6 
personnelle dans le maniement de cette methode est tres r6elle. II sait 
scruter les statistiques d'une fagon fort p^n^trante et exposer les r6- 
sultats de ses recherches avec beaucoup d'el^gance. Le lecteiu* frangais 
en particulier, appreciera ringeniosit6 avec laquelle il tire des statistiques 
frangaises des inductions souvent nouvelles et justes." Albert Afta- 
LioN, in the Revue d'histoire des doctrines Sconomiques. 

"Alcuni dei risultati ottenuti dall'autore, sono nuovi e suggestivi 
e da essi molte conclusioni si possono trarre (cui I'autore accenna nel 
capitolo finale della sua opera) sia rispetto alle teorie del salario che 
rispetto alia poUtica sociale. II libro e insomma, ripetiamo, un con- 
tributo molto importante all'investigazione scientifica dei fenomeni 
economici e vorremmo che esso stimolasse parecchi altri studiosi a fare 
per altre industrie o per altri paesi, recerche analoghe. Constantino 
Bresciani Turroni, in the Giornale degli Economisti. 



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